Trigonometric Inequality: -3/2 ≤ cosα + cosβ + cosγ ≤ 3
2017-10-14 05:15
This GeoGebra applet demonstrates the trigonometric inequality -3/2 ≤ cosα + cosβ + cosγ ≤ 3 through geometric construction and vector analysis. Using points A, B, C, D and their corresponding vectors, it visualizes angular relationships and allows interactive exploration of the cosine sum's range and boundary conditions via sliders. Ideal for teaching trigonometric inequality proofs, math competi
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<command name="PointIn">
<input a0="b"/>
<output a0="P"/>
</command>
<element type="point3d" label="P">
<show object="true" label="false" ev="4"/>
<condition showObject="showGlobal"/>
<objColor r="0" g="0" b="204" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="-2.3368637071388263" y="-2.458031289646729" z="-1.0" w="1.0"/>
<pointSize val="5"/>
</element>
<command name="Point">
<input a0="Ray[P, P + (0, 0, 1)]"/>
<output a0="Q"/>
</command>
<element type="point3d" label="Q">
<show object="true" label="false" ev="4"/>
<condition showObject="showGlobal"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="-2.3368637071388263" y="-2.458031289646729" z="0.0" w="1.0"/>
<pointSize val="5"/>
</element>
<expression label="level" exp="z = z(Q)" type="plane" />
<element type="plane3d" label="level">
<show object="true" label="false" ev="4"/>
<condition showObject="showGlobal"/>
<objColor r="153" g="204" b="255" alpha="0.6000000238418579"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<coords x="0.0" y="0.0" z="1.0" w="-0.0"/>
<fading val="0.0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<command name="IntersectPath">
<input a0="level" a1="f"/>
<output a0="leveCurve"/>
</command>
<element type="implicitpoly" label="leveCurve">
<show object="true" label="true" ev="4"/>
<condition showObject="showGlobal"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="4"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="2"/>
<userinput show="false"/></element>
<command name="Segment">
<input a0="P" a1="Q"/>
<output a0="segLevel"/>
</command>
<element type="segment3d" label="segLevel">
<show object="true" label="false" ev="4"/>
<condition showObject="showGlobal"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text6" exp=""z=" + (LaTeX[z(Q)]) + """ />
<element type="text" label="text6">
<show object="true" label="false" ev="20"/>
<condition showObject="showGlobal"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="5" style="1"/>
<startPoint exp="Q"/>
<labelOffset x="-28" y="-45"/>
</element>
</construction>
</geogebra>