三角函数图像变换动画演示
2018-01-07 04:24
本范例通过动态动画直观演示三角函数图像的变换过程。通过调整相关参数，用户可以观察振幅、周期、相位等变化对三角函数图像的影响，深入理解函数的平移、伸缩等几何变换规律，是辅助高中三角函数教学的优质互动工具。
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="5.0.414.0" app="classic" platform="d" id="28e94f3a-2d9b-42bd-a5a9-5df9d931189c" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1382" height="784" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.0723589001447178" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="162,89,700,550" />
<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="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="1" visible="true" inframe="false" stylebar="true" location="1" size="1250" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="100" window="100,100,250,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" 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="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" 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="true" cmd="true" top="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1250" height="591"/>
<coordSystem xZero="121.22190327666767" yZero="271.3882097063155" scale="58.982199772274235" yscale="58.98219977227424"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<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="true" label="" unitLabel="" tickStyle="2" showNumbers="false"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="2" showNumbers="false"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="ω">
<value val="0.8"/>
<symbolic val="true" />
<show object="true" label="true"/>
<objColor r="127" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0.5" max="2" width="4.0" x="1.5225447720138143" y="3.9960635531945488" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.05" speed="1" type="0" playing="true"/>
</element>
<element type="numeric" label="A">
<value val="0.9"/>
<symbolic val="true" />
<show object="true" label="true"/>
<objColor r="0" g="255" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0.5" max="2" width="4.0" x="1.4892354156476613" y="3.2410144939169996" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.05" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="φ">
<value val="0.0"/>
<symbolic val="true" />
<show object="true" label="true"/>
<objColor r="153" g="51" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="(-π)" max="π" width="4.0" x="1.4765867907310641" y="2.6591777477535308" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="π / 20" speed="1" type="0" playing="false"/>
</element>
<expression label ="h" exp="h: x = π + sqrt(y) - sqrt(y) + sqrt(0.2 - y) - sqrt(0.2 - y)"/>
<expression label ="h" exp="x = π + sqrt(y) - sqrt(y) + sqrt(0.2 - y) - sqrt(0.2 - y)"/>
<element type="implicitpoly" label="h">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-11" y="47"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<userinput show="false"/></element>
<expression label ="g" exp="g: x = π / 2 + sqrt(y) - sqrt(y) + sqrt(0.2 - y) - sqrt(0.2 - y)"/>
<expression label ="g" exp="x = π / 2 + sqrt(y) - sqrt(y) + sqrt(0.2 - y) - sqrt(0.2 - y)"/>
<element type="implicitpoly" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<userinput show="false"/></element>
<expression label ="j" exp="j: x = (2 * π) + sqrt(y) - sqrt(y) + sqrt(0.2 - y) - sqrt(0.2 - y)"/>
<expression label ="j" exp="x = (2 * π) + sqrt(y) - sqrt(y) + sqrt(0.2 - y) - sqrt(0.2 - y)"/>
<element type="implicitpoly" label="j">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<userinput show="false"/></element>
<expression label ="k" exp="k: x = (4 * π) + sqrt(y) - sqrt(y) + sqrt(0.2 - y) - sqrt(0.2 - y)"/>
<expression label ="k" exp="x = (4 * π) + sqrt(y) - sqrt(y) + sqrt(0.2 - y) - sqrt(0.2 - y)"/>
<element type="implicitpoly" label="k">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<userinput show="false"/></element>
<expression label ="i" exp="i: x = (3 * π / 2) + sqrt(y) - sqrt(y) + sqrt(0.2 - y) - sqrt(0.2 - y)"/>
<expression label ="i" exp="x = (3 * π / 2) + sqrt(y) - sqrt(y) + sqrt(0.2 - y) - sqrt(0.2 - y)"/>
<element type="implicitpoly" label="i">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<userinput show="false"/></element>
<expression label ="l" exp="l: x = (3 * π) + sqrt(y) - sqrt(y) + sqrt(0.2 - y) - sqrt(0.2 - y)"/>
<expression label ="l" exp="x = (3 * π) + sqrt(y) - sqrt(y) + sqrt(0.2 - y) - sqrt(0.2 - y)"/>
<element type="implicitpoly" label="l">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<userinput show="false"/></element>
<expression label ="m" exp="y = 1" type="line"/>
<element type="line" label="m">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="0.0" y="1.0" z="-1.0"/>
<lineStyle thickness="5" type="20" typeHidden="1"/>
<eqnStyle style="explicit"/>
</element>
<expression label ="n" exp="y = -1" type="line"/>
<element type="line" label="n">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="0.0" y="1.0" z="1.0"/>
<lineStyle thickness="5" type="20" typeHidden="1"/>
<eqnStyle style="explicit"/>
</element>
<expression label ="q" exp="y = 2" type="line"/>
<element type="line" label="q">
<show object="true" label="false" ev="4"/>
<objColor r="128" g="128" b="128" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="0.0" y="1.0" z="-2.0"/>
<lineStyle thickness="5" type="20" typeHidden="1"/>
<eqnStyle style="explicit"/>
</element>
<expression label ="r" exp="y = -2" type="line"/>
<element type="line" label="r">
<show object="true" label="false" ev="4"/>
<objColor r="128" g="128" b="128" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="0.0" y="1.0" z="2.0"/>
<lineStyle thickness="5" type="20" typeHidden="1"/>
<eqnStyle style="explicit"/>
</element>
<expression label ="s" exp="y = 1 / 2" type="line"/>
<element type="line" label="s">
<show object="true" label="false" ev="4"/>
<objColor r="128" g="128" b="128" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="0.0" y="1.0" z="-0.5"/>
<lineStyle thickness="5" type="20" typeHidden="1"/>
<eqnStyle style="explicit"/>
</element>
<expression label ="t" exp="y = -1 / 2" type="line"/>
<element type="line" label="t">
<show object="true" label="false" ev="4"/>
<objColor r="128" g="128" b="128" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="0.0" y="1.0" z="0.5"/>
<lineStyle thickness="5" type="20" typeHidden="1"/>
<eqnStyle style="explicit"/>
</element>
<expression label="文本1" exp=""y=Asin(ωx+φ)""/>
<element type="text" label="文本1">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="102" b="51" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="4.0" size="36" style="3"/>
<startPoint x="7.147396813426763" y="3.6218520825109954" z="1.0"/>
</element>
<expression label="文本2" exp=""y=" + (LaTeX[A]) + "sin(" + (LaTeX[ω]) + "x+" + (LaTeX[φ]) + ")"" />
<element type="text" label="文本2">
<show object="true" label="true" ev="40"/>
<objColor r="255" g="0" b="51" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="7.105283446021337" y="3.1176533609764197" z="1.0"/>
</element>
<expression label ="f_1" exp="f_1(x) = If[0 ≤ x ≤ (2 * π), sin(x)]" type="function"/>
<element type="function" label="f_1">
<show object="true" label="false" ev="4"/>
<objColor r="153" g="51" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<lineStyle thickness="5" type="20" typeHidden="1"/>
</element>
<expression label="g_1" exp="g_1(x) = If[((-φ)) / ω < x < (2 * π / ω) - φ / ω, (A * sin((ω * x) + φ))]" />
<element type="function" label="g_1">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="80" y="1"/>
<labelMode val="1"/>
<isShape val="false"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
</element>
<expression label="文本3" exp=""π""/>
<element type="text" label="文本3">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="2.778263566906877" y="0.03832289751741805" z="1.0"/>
</element>
<expression label="文本4" exp=""\frac{π}{2}""/>
<element type="text" label="文本4">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="5" style="1"/>
<startPoint x="1.335522823838254" y="-0.004170015378247988" z="1.0"/>
</element>
<expression label="文本3_1" exp=""2π""/>
<element type="text" label="文本3_1">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="5.89529603649958" y="0.09175773985329291" z="1.0"/>
</element>
<expression label="文本4_1" exp=""\frac{3π}{2}""/>
<element type="text" label="文本4_1">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="5" style="1"/>
<startPoint x="4.41693206520704" y="-0.03292355893041499" z="1.0"/>
</element>
<expression label="文本3_2" exp=""3π""/>
<element type="text" label="文本3_2">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="9.0" y="0.0" z="1.0"/>
</element>
<expression label="文本3_3" exp=""4π""/>
<element type="text" label="文本3_3">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="12.182795818020862" y="0.0026996692935015477" z="1.0"/>
</element>
<expression label="文本3_4" exp=""2""/>
<element type="text" label="文本3_4">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="-0.5284967905066295" y="2.345283666312373" z="1.0"/>
</element>
<expression label="文本3_5" exp=""1""/>
<element type="text" label="文本3_5">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="-0.48746746285619524" y="1.3990358112263028" z="1.0"/>
</element>
<expression label="文本4_2" exp=""\frac{1}{2}""/>
<element type="text" label="文本4_2">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint x="-0.40540880755532693" y="0.8246252241202258" z="1.0"/>
</element>
<expression label="文本4_3" exp=""-\frac{1}{2}""/>
<element type="text" label="文本4_3">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="1"/>
<startPoint x="-0.7438648160796757" y="-0.036990656538890686" z="1.0"/>
</element>
<expression label="文本3_6" exp=""-1""/>
<element type="text" label="文本3_6">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="-0.946438135205761" y="-0.6319159074701853" z="1.0"/>
</element>
<expression label="文本3_7" exp=""-2""/>
<element type="text" label="文本3_7">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="12" style="1"/>
<startPoint x="-0.992614101108366" y="-1.616619771080604" z="1.0"/>
</element>
</construction>
</geogebra>