三角函数周期与振幅变化演示
2020-11-17 14:24
本范例专为课堂投影教学设计，直观展示三角函数的周期和振幅变化规律。通过动态调整参数，用户可以清晰观察正弦、余弦等函数图像的伸缩与平移。该工具适合中学数学课堂辅助教学，帮助学生深入理解三角函数的图像性质及其参数的几何意义。
GeoGebra 画板及绘图内容加载中，请稍等……
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.672.0" app="classic" platform="w" id="772f0093-06f5-40d5-bc49-0b5d6528c5af" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1222" height="514" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.6407528641571195" orientation="1" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3,3" size="335" tab="ALGEBRA" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="395" window="610,240,700,550" />
<view id="1" visible="true" inframe="false" stylebar="false" location="3" size="783" window="100,100,600,400" />
<view id="16" visible="true" inframe="false" stylebar="false" location="1" size="431" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="24"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="782" height="512"/>
<coordSystem xZero="361.89868556901547" yZero="317.82220568794406" scale="65.18709667214287" yscale="65.18709667214264"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="0" g="0" b="0"/>
<axesColor r="255" g="255" b="255"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="3" grid="0"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1.5707963267948966" tickExpression="π / 2"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1" tickExpression="1"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="430" height="512"/>
<coordSystem xZero="-523.8379448770303" yZero="-187.2191269818005" scale="56.39105883766963" yscale="1127.8211767533985"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="k">
<value val="1"/>
<symbolic val="true" />
<show object="true" label="true" ev="3"/>
<objColor r="51" g="255" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="130" x="10" y="229" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="a">
<value val="1"/>
<symbolic val="true" />
<show object="true" label="true" ev="3"/>
<objColor r="255" g="0" b="51" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="130" x="162" y="226" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="b">
<value val="0"/>
<symbolic val="true" />
<show object="true" label="true" ev="3"/>
<objColor r="0" g="153" b="204" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="(-5 * π)" max="(5 * π)" absoluteScreenLocation="true" width="130" x="11" y="274" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="π / 36" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="c">
<value val="0"/>
<symbolic val="true" />
<show object="true" label="true" ev="3"/>
<objColor r="255" g="102" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="130" x="164" y="274" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<expression label="text3_1" exp=""y=\textcolor{0,153,0}{k} \sin \left(\textcolor{204,0,0}{a}(x+\textcolor{0,153,204}{b})\right)+\textcolor{255,102,0}{c}""/>
<element type="text" label="text3_1">
<show object="true" label="true" ev="43"/>
<condition showObject="si ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="135" y="3"/>
</element>
<expression label="text3_2" exp=""y=\textcolor{0,153,0}{k} \cos \left(\textcolor{204,0,0}{a}(x+\textcolor{0,153,204}{b})\right)+\textcolor{255,102,0}{c}""/>
<element type="text" label="text3_2">
<show object="true" label="true" ev="43"/>
<condition showObject="co ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="134" y="34"/>
</element>
<expression label="text3_3" exp=""y=\textcolor{0,153,0}{k} \tan \left(\textcolor{204,0,0}{a}(x+\textcolor{0,153,204}{b})\right)+\textcolor{255,102,0}{c}""/>
<element type="text" label="text3_3">
<show object="true" label="true" ev="43"/>
<condition showObject="ta ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="134" y="63"/>
</element>
<expression label="text3_4" exp=""y=\textcolor{0,153,0}{k} \cot \left(\textcolor{204,0,0}{a}(x+\textcolor{0,153,204}{b})\right)+\textcolor{255,102,0}{c}""/>
<element type="text" label="text3_4">
<show object="true" label="true" ev="43"/>
<condition showObject="ct ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="133" y="97"/>
</element>
<expression label="text3_5" exp=""y=\textcolor{0,153,0}{k} \sec \left(\textcolor{204,0,0}{a}(x+\textcolor{0,153,204}{b})\right)+\textcolor{255,102,0}{c}""/>
<element type="text" label="text3_5">
<show object="true" label="true" ev="43"/>
<condition showObject="se ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="135" y="132"/>
</element>
<element type="boolean" label="si">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="2" y="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="If(!oo&&si,SetValue(osi,true),If(!oo&&!si,SetValue(osi,false)))
"/>
<caption val="正弦函數"/>
</element>
<element type="boolean" label="co">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="2" y="33"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="If(!oo&&co,SetValue(oco,true),If(!oo&&!co,SetValue(oco,false)))"/>
<caption val="餘弦函數"/>
</element>
<element type="boolean" label="ta">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="3" y="65"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="If(!oo&&ta,SetValue(ota,true),If(!oo&&!ta,SetValue(ota,false)))"/>
<caption val="正切函數"/>
</element>
<element type="boolean" label="ct">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="3" y="97"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="If(!oo&&ct,SetValue(oct,true),If(!oo&&!ct,SetValue(oct,false)))"/>
<caption val="餘切函數"/>
</element>
<element type="boolean" label="se">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="4" y="129"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="If(!oo&&se,SetValue(ose,true),If(!oo&&!se,SetValue(ose,false)))"/>
<caption val="正割函數"/>
</element>
<expression label="text3_6" exp=""y=\textcolor{0,153,0}{k} \csc \left(\textcolor{204,0,0}{a}(x+\textcolor{0,153,204}{b})\right)+\textcolor{255,102,0}{c}""/>
<element type="text" label="text3_6">
<show object="true" label="true" ev="43"/>
<condition showObject="cc ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="134" y="161"/>
</element>
<element type="boolean" label="cc">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="3" y="161"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="If(!oo&&cc,SetValue(occ,true),If(!oo&&!cc,SetValue(occ,false)))"/>
<caption val="餘割函數"/>
</element>
<expression label="list_2" exp="{y = k + c, y = (-k) + c}" />
<element type="list" label="list_2">
<show object="true" label="true" ev="8"/>
<condition showObject="(si ∨ co ∨ se ∨ cc) ∧ e"/>
<objColor r="224" g="224" b="224" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="10" type="15" typeHidden="1" opacity="204"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<element type="button" label="button1">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="238" y="286"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(k,1)
SetValue(a,1)
SetValue(b,0)
SetValue(c,0)
SetValue(si,true)
SetValue(co,false)
SetValue(ta,false)
SetValue(ct,false)
SetValue(se,false)
SetValue(cc,false)
SetValue(oo,false)
SetValue(d,true)
SetValue(e,true)
SetValue(lab,true)
SetValue(cir,true)
SetValue(osi,true)
SetValue(oco,false)
SetValue(ota,false)
SetValue(oct,false)
SetValue(ose,false)
SetValue(occ,false)"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="Reset"/>
</element>
<command name="Sequence">
<input a0="x = ((i * 2) * π / a)" a1="i" a2="-30" a3="30"/>
<output a0="list_1" randomResult="{x = -188.49555921538757, x = -182.212373908208, x = -175.92918860102841, x = -169.64600329384882, x = -163.36281798666926, x = -157.07963267948966, x = -150.79644737231007, x = -144.51326206513048, x = -138.23007675795088, x = -131.94689145077132, x = -125.66370614359172, x = -119.38052083641213, x = -113.09733552923255, x = -106.81415022205297, x = -100.53096491487338, x = -94.24777960769379, x = -87.96459430051421, x = -81.68140899333463, x = -75.39822368615503, x = -69.11503837897544, x = -62.83185307179586, x = -56.548667764616276, x = -50.26548245743669, x = -43.982297150257104, x = -37.69911184307752, x = -31.41592653589793, x = -25.132741228718345, x = -18.84955592153876, x = -12.566370614359172, x = -6.283185307179586, x = 0, x = 6.283185307179586, x = 12.566370614359172, x = 18.84955592153876, x = 25.132741228718345, x = 31.41592653589793, x = 37.69911184307752, x = 43.982297150257104, x = 50.26548245743669, x = 56.548667764616276, x = 62.83185307179586, x = 69.11503837897544, x = 75.39822368615503, x = 81.68140899333463, x = 87.96459430051421, x = 94.24777960769379, x = 100.53096491487338, x = 106.81415022205297, x = 113.09733552923255, x = 119.38052083641213, x = 125.66370614359172, x = 131.94689145077132, x = 138.23007675795088, x = 144.51326206513048, x = 150.79644737231007, x = 157.07963267948966, x = 163.36281798666926, x = 169.64600329384882, x = 175.92918860102841, x = 182.212373908208, x = 188.49555921538757}"/>
</command>
<element type="list" label="list_1">
<show object="true" label="true" ev="8"/>
<condition showObject="(si ∨ co ∨ se ∨ cc) ∧ cir"/>
<objColor r="255" g="239" b="213" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="9" type="10" typeHidden="1" opacity="178"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<element type="boolean" label="lab">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="5" y="323"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="函數標籤"/>
</element>
<element type="boolean" label="cir">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="8" y="359"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="週期界線"/>
</element>
<element type="boolean" label="d">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<condition showObject="ta ∨ ct ∨ se ∨ cc"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="145" y="325"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="漸近線"/>
</element>
<element type="boolean" label="e">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<condition showObject="si ∨ co ∨ se ∨ cc"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="146" y="359"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="範圍"/>
</element>
<command name="Textfield">
<input a0="b"/>
<output a0="inputBox1"/>
</command>
<element type="textfield" label="inputBox1">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="4" y="284"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<length val="4"/>
<caption val="調控或輸入b="/>
</element>
<expression label="p" exp="p(x) = sin(x)" type="function"/>
<element type="function" label="p">
<show object="true" label="false" ev="4"/>
<condition showObject="oo ∧ osi"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="10" type="20" typeHidden="1" opacity="178"/>
</element>
<expression label="q" exp="q(x) = cos(x)" type="function"/>
<element type="function" label="q">
<show object="true" label="false" ev="8"/>
<condition showObject="oo ∧ oco"/>
<objColor r="255" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="10" type="20" typeHidden="1" opacity="178"/>
</element>
<expression label="r" exp="r(x) = tan(x)" type="function"/>
<element type="function" label="r">
<show object="true" label="false" ev="4"/>
<condition showObject="oo ∧ ota"/>
<objColor r="204" g="102" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="10" type="20" typeHidden="1" opacity="178"/>
</element>
<expression label="f_1" exp="f_1(x) = cot(x)" type="function"/>
<element type="function" label="f_1">
<show object="true" label="false" ev="4"/>
<condition showObject="oo ∧ oct"/>
<objColor r="204" g="153" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="10" type="20" typeHidden="1" opacity="178"/>
</element>
<expression label="g_1" exp="g_1(x) = sec(x)" type="function"/>
<element type="function" label="g_1">
<show object="true" label="false" ev="4"/>
<condition showObject="oo ∧ ose"/>
<objColor r="102" g="204" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="10" type="20" typeHidden="1" opacity="178"/>
</element>
<expression label="h_1" exp="h_1(x) = csc(x)" type="function"/>
<element type="function" label="h_1">
<show object="true" label="false" ev="4"/>
<condition showObject="oo ∧ occ"/>
<objColor r="175" g="238" b="238" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="10" type="20" typeHidden="1" opacity="178"/>
</element>
<element type="boolean" label="oo">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="236" y="361"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="顯示原始函數"/>
</element>
<element type="boolean" label="osi">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<condition showObject="oo ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="6" y="388"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="sin(x)"/>
</element>
<element type="boolean" label="oco">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<condition showObject="oo ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="6" y="419"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="cos(x)"/>
</element>
<element type="boolean" label="ota">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<condition showObject="oo ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="109" y="387"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="tan(x)"/>
</element>
<element type="boolean" label="oct">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<condition showObject="oo ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="109" y="421"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="cot(x)"/>
</element>
<element type="boolean" label="ose">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<condition showObject="oo ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="206" y="391"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="sec(x)"/>
</element>
<element type="boolean" label="occ">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<condition showObject="oo ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="206" y="421"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="csc(x)"/>
</element>
<expression label="f" exp="f(x) = (k * sin((a * (x + b)))) + c" />
<element type="function" label="f">
<show object="true" label="false" ev="4"/>
<condition showObject="si ≠ 0"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
</element>
<expression label="g" exp="g(x) = (k * cos((a * (x + b)))) + c" />
<element type="function" label="g">
<show object="true" label="false" ev="4"/>
<condition showObject="co ≠ 0"/>
<objColor r="255" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
</element>
<expression label="h" exp="h(x) = (k * tan((a * (x + b)))) + c" />
<element type="function" label="h">
<show object="true" label="false" ev="4"/>
<condition showObject="ta ≠ 0"/>
<objColor r="204" g="102" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
</element>
<expression label="s" exp="s(x) = (k * cot((a * (x + b)))) + c" />
<element type="function" label="s">
<show object="true" label="false" ev="8"/>
<condition showObject="ct ≠ 0"/>
<objColor r="204" g="153" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
</element>
<expression label="t" exp="t(x) = (k * sec((a * (x + b)))) + c" />
<element type="function" label="t">
<show object="true" label="false" ev="8"/>
<condition showObject="se ≠ 0"/>
<objColor r="0" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
</element>
<expression label="u" exp="u(x) = (k * csc((a * (x + b)))) + c" />
<element type="function" label="u">
<show object="true" label="false" ev="8"/>
<condition showObject="cc ≠ 0"/>
<objColor r="175" g="238" b="238" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
</element>
<command name="Sequence">
<input a0="x = ((i * π) + π / 2) / a - b" a1="i" a2="-40" a3="40"/>
<output a0="list_3" randomResult="{x = -124.09290981679683, x = -120.95131716320704, x = -117.80972450961724, x = -114.66813185602746, x = -111.52653920243766, x = -108.38494654884786, x = -105.24335389525808, x = -102.10176124166829, x = -98.96016858807849, x = -95.81857593448869, x = -92.6769832808989, x = -89.53539062730911, x = -86.39379797371932, x = -83.25220532012952, x = -80.11061266653974, x = -76.96902001294994, x = -73.82742735936014, x = -70.68583470577035, x = -67.54424205218055, x = -64.40264939859077, x = -61.261056745000964, x = -58.11946409141117, x = -54.97787143782138, x = -51.83627878423159, x = -48.69468613064179, x = -45.553093477051995, x = -42.411500823462205, x = -39.269908169872416, x = -36.12831551628262, x = -32.98672286269282, x = -29.845130209103033, x = -26.703537555513243, x = -23.561944901923447, x = -20.420352248333657, x = -17.27875959474386, x = -14.137166941154069, x = -10.995574287564276, x = -7.853981633974483, x = -4.71238898038469, x = -1.5707963267948966, x = 1.5707963267948966, x = 4.71238898038469, x = 7.853981633974483, x = 10.995574287564276, x = 14.137166941154069, x = 17.27875959474386, x = 20.420352248333657, x = 23.561944901923447, x = 26.703537555513243, x = 29.845130209103033, x = 32.98672286269283, x = 36.12831551628262, x = 39.269908169872416, x = 42.41150082346221, x = 45.553093477052, x = 48.69468613064179, x = 51.83627878423159, x = 54.977871437821385, x = 58.119464091411174, x = 61.261056745000964, x = 64.40264939859075, x = 67.54424205218055, x = 70.68583470577033, x = 73.82742735936013, x = 76.96902001294993, x = 80.11061266653972, x = 83.25220532012952, x = 86.3937979737193, x = 89.5353906273091, x = 92.6769832808989, x = 95.81857593448868, x = 98.96016858807847, x = 102.10176124166827, x = 105.24335389525807, x = 108.38494654884786, x = 111.52653920243765, x = 114.66813185602744, x = 117.80972450961724, x = 120.95131716320702, x = 124.09290981679682, x = 127.23450247038662}"/>
</command>
<element type="list" label="list_3">
<show object="false" label="true" ev="8"/>
<condition showObject="ta ∧ (d ∨ cir) ∨ se ∧ d"/>
<objColor r="102" g="204" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="10" type="10" typeHidden="1" opacity="204"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="x = ((i * π)) / a - b" a1="i" a2="-40" a3="40"/>
<output a0="list_4" randomResult="{x = -125.66370614359172, x = -122.52211349000193, x = -119.38052083641213, x = -116.23892818282235, x = -113.09733552923255, x = -109.95574287564276, x = -106.81415022205297, x = -103.67255756846318, x = -100.53096491487338, x = -97.38937226128358, x = -94.24777960769379, x = -91.106186954104, x = -87.96459430051421, x = -84.82300164692441, x = -81.68140899333463, x = -78.53981633974483, x = -75.39822368615503, x = -72.25663103256524, x = -69.11503837897544, x = -65.97344572538566, x = -62.83185307179586, x = -59.690260418206066, x = -56.548667764616276, x = -53.40707511102649, x = -50.26548245743669, x = -47.12388980384689, x = -43.982297150257104, x = -40.840704496667314, x = -37.69911184307752, x = -34.55751918948772, x = -31.41592653589793, x = -28.274333882308138, x = -25.132741228718345, x = -21.991148575128552, x = -18.84955592153876, x = -15.707963267948966, x = -12.566370614359172, x = -9.42477796076938, x = -6.283185307179586, x = -3.141592653589793, x = 0, x = 3.141592653589793, x = 6.283185307179586, x = 9.42477796076938, x = 12.566370614359172, x = 15.707963267948966, x = 18.84955592153876, x = 21.991148575128552, x = 25.132741228718345, x = 28.274333882308138, x = 31.41592653589793, x = 34.55751918948772, x = 37.69911184307752, x = 40.840704496667314, x = 43.982297150257104, x = 47.12388980384689, x = 50.26548245743669, x = 53.40707511102649, x = 56.548667764616276, x = 59.690260418206066, x = 62.83185307179586, x = 65.97344572538566, x = 69.11503837897544, x = 72.25663103256524, x = 75.39822368615503, x = 78.53981633974483, x = 81.68140899333463, x = 84.82300164692441, x = 87.96459430051421, x = 91.106186954104, x = 94.24777960769379, x = 97.38937226128358, x = 100.53096491487338, x = 103.67255756846318, x = 106.81415022205297, x = 109.95574287564276, x = 113.09733552923255, x = 116.23892818282235, x = 119.38052083641213, x = 122.52211349000193, x = 125.66370614359172}"/>
</command>
<element type="list" label="list_4">
<show object="true" label="false" ev="4"/>
<condition showObject="(cc ∨ ct) ∧ (d ∨ cir ∧ ct)"/>
<objColor r="153" g="255" b="153" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="10" type="10" typeHidden="1" opacity="204"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<element type="boolean" label="i">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="6" y="465"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="大標籤"/>
</element>
<expression label="text2" exp=""\textcolor{51,255,0}{k}\text{" + (LaTeX[If[si, "sin", If[co, "cos", If[ta, "tan", If[ct, "cot", If[se, "sec", If[cc, "csc", "sin"]]]]]]]) + "}(\textcolor{255,0,0}{a}(x+\textcolor{102,204,255}{b}))+\textcolor{255,102,0}{c}"" />
<element type="text" label="text2">
<show object="true" label="false" ev="8"/>
<condition showObject="i"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<bgColor r="0" g="0" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.8" size="44" style="1"/>
<absoluteScreenLocation x="80" y="4"/>
</element>
<expression label="text1" exp=""y=\textcolor{51,255,0}{" + (LaTeX[If[k ≟ 1, "", "" + k]]) + "}\sin\left(\textcolor{255,0,0}{" + (LaTeX[If[a ≟ 1, "", "" + a]]) + "}" + (LaTeX[If[a ≟ 1, If[b > 0, "x+", "x"], If[b ≟ 0, "x", If[b > 0, "(x+", "(x"]]]]) + " \textcolor{102,204,255}{" + (LaTeX[If[b ≟ 0, "", "" + ((b * 36 / π)) + "π /36"]]) + "}" + (LaTeX[If[((a - 1) * b) ≟ 0, "", ")"]]) + "\right)" + (LaTeX[If[c > 0, "+", ""]]) + "\textcolor{255,102,0}{" + (LaTeX[If[c ≟ 0, "", "" + c]]) + "}"" />
<element type="text" label="text1">
<show object="true" label="true" ev="8"/>
<condition showObject="si ∧ lab"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.5" size="12" style="1"/>
<startPoint x="-1.9252372910286994" y="1.7817958446804958" z="1"/>
</element>
<expression label="text6_1" exp=""y=\textcolor{51,255,0}{" + (LaTeX[If[k ≟ 1, "", "" + k]]) + "}\tan\left(\textcolor{255,0,0}{" + (LaTeX[If[a ≟ 1, "", "" + a]]) + "}" + (LaTeX[If[a ≟ 1, If[b > 0, "x+", "x"], If[b ≟ 0, "x", If[b > 0, "(x+", "(x"]]]]) + "\textcolor{102,204,255}{" + (LaTeX[If[b ≟ 0, "", "" + ((b * 36 / π)) + "π /36"]]) + "}" + (LaTeX[If[((a - 1) * b) ≟ 0, "", ")"]]) + "\right)" + (LaTeX[If[c > 0, "+", ""]]) + "\textcolor{255,102,0}{" + (LaTeX[If[c ≟ 0, "", "" + c]]) + "}"" />
<element type="text" label="text6_1">
<show object="false" label="true" ev="8"/>
<condition showObject="ta ∧ lab"/>
<objColor r="204" g="102" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.5" size="12" style="1"/>
<startPoint x="-3.096665143430112" y="2.9622542142865687" z="1"/>
</element>
<expression label="text7_1" exp=""y=\textcolor{51,255,0}{" + (LaTeX[If[k ≟ 1, "", "" + k]]) + "} \cot\left(\textcolor{255,0,0}{" + (LaTeX[If[a ≟ 1, "", "" + a]]) + "}" + (LaTeX[If[a ≟ 1, If[b > 0, "x+", "x"], If[b ≟ 0, "x", If[b > 0, "(x+", "(x"]]]]) + "\textcolor{102,204,255}{" + (LaTeX[If[b ≟ 0, "", "" + ((b * 36 / π)) + "π /36"]]) + "}" + (LaTeX[If[((a - 1) * b) ≟ 0, "", ")"]]) + "\right)" + (LaTeX[If[c > 0, "+", ""]]) + "\textcolor{255,102,0}{" + (LaTeX[If[c ≟ 0, "", "" + c]]) + "}"" />
<element type="text" label="text7_1">
<show object="true" label="true" ev="8"/>
<condition showObject="ct ∧ lab"/>
<objColor r="204" g="153" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.5" size="12" style="1"/>
<startPoint x="-1.4089087051830052" y="0.30403215847669895" z="1"/>
</element>
<expression label="text9_1" exp=""y=\textcolor{51,255,0}{" + (LaTeX[If[k ≟ 1, "", "" + k]]) + "} \csc\left(\textcolor{255,0,0}{" + (LaTeX[If[a ≟ 1, "", "" + a]]) + "}" + (LaTeX[If[a ≟ 1, If[b > 0, "x+", "x"], If[b ≟ 0, "x", If[b > 0, "(x+", "(x"]]]]) + "\textcolor{102,204,255}{" + (LaTeX[If[b ≟ 0, "", "" + ((b * 36 / π)) + "π /36"]]) + "}" + (LaTeX[If[((a - 1) * b) ≟ 0, "", ")"]]) + "\right)" + (LaTeX[If[c > 0, "+", ""]]) + "\textcolor{255,102,0}{" + (LaTeX[If[c ≟ 0, "", "" + c]]) + "}"" />
<element type="text" label="text9_1">
<show object="true" label="true" ev="8"/>
<condition showObject="cc ∧ lab"/>
<objColor r="175" g="238" b="238" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.5" size="12" style="1"/>
<startPoint x="-2.2986315557183876" y="1.151939198523329" z="1"/>
</element>
<expression label="text5_1" exp=""y=\textcolor{51,255,0}{" + (LaTeX[If[k ≟ 1, "", "" + k]]) + "}\cos\left(\textcolor{255,0,0}{" + (LaTeX[If[a ≟ 1, "", "" + a]]) + "}" + (LaTeX[If[a ≟ 1, If[b > 0, "x+", "x"], If[b ≟ 0, "x", If[b > 0, "(x+", "(x"]]]]) + " \textcolor{102,204,255}{" + (LaTeX[If[b ≟ 0, "", "" + ((b * 36 / π)) + "π /36"]]) + "}" + (LaTeX[If[((a - 1) * b) ≟ 0, "", ")"]]) + "\right)" + (LaTeX[If[c > 0, "+", ""]]) + "\textcolor{255,102,0}{" + (LaTeX[If[c ≟ 0, "", "" + c]]) + "}"" />
<element type="text" label="text5_1">
<show object="true" label="true" ev="8"/>
<condition showObject="co ∧ lab"/>
<objColor r="255" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.5" size="12" style="1"/>
<startPoint x="-1.207681219618264" y="-0.9544364722770295" z="1"/>
</element>
<expression label="text8_1" exp=""y=\textcolor{51,255,0}{" + (LaTeX[If[k ≟ 1, "", "" + k]]) + "} \sec\left(\textcolor{255,0,0}{" + (LaTeX[If[a ≟ 1, "", "" + a]]) + "}" + (LaTeX[If[a ≟ 1, If[b > 0, "x+", "x"], If[b ≟ 0, "x", If[b > 0, "(x+", "(x"]]]]) + "\textcolor{102,204,255}{" + (LaTeX[If[b ≟ 0, "", "" + ((b * 36 / π)) + "π /36"]]) + "}" + (LaTeX[If[((a - 1) * b) ≟ 0, "", ")"]]) + "\right)" + (LaTeX[If[c > 0, "+", ""]]) + "\textcolor{255,102,0}{" + (LaTeX[If[c ≟ 0, "", "" + c]]) + """ />
<element type="text" label="text8_1">
<show object="true" label="true" ev="8"/>
<condition showObject="se ∧ lab"/>
<objColor r="0" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.5" size="12" style="1"/>
<startPoint x="-2.1598705451573688" y="-1.484810965816052" z="1"/>
</element>
</construction>
</geogebra>