Exact Values of Trigonometric Functions
2014-12-17 05:30
This GeoGebra applet demonstrates how to derive and visualize the exact values of trigonometric functions using geometric constructions such as circles, triangles, polygons, and vectors. By calculating intersections, segments, distances, and angles, it intuitively presents the geometric meaning and exact numerical values of trigonometric functions at specific angles, making it ideal for teaching a
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<expression label="o" exp="round(round(α) / 30) ≟ round(α) / 30" />
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<expression label="fortyfiveAngle" exp="round(α) ≟ 135° ∨ round(α) ≟ 225° ∨ round(α) ≟ 315°" />
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<expression label="text36" exp=""sin(" + (LaTeX[α]) + ")=" + (LaTeX[Element[sinValues, angleIndex]]) + """ />
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<expression label="text35" exp=""cos( " + (LaTeX[α]) + ")=" + (LaTeX[Element[cosValues, angleIndex]]) + """ />
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<expression label="text9" exp=""\left(\fgcolor{" + (LaTeX[xColour]) + "}{-\frac{\sqrt{2}}{2}},\fgcolor{" + (LaTeX[yColour]) + "}{\frac{\sqrt{2}}{2}}\right) "" />
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<expression label="text10" exp=""\left(\fgcolor{" + (LaTeX[xColour]) + "}{-\frac{\sqrt{2}}{2}},\fgcolor{" + (LaTeX[yColour]) + "}{-\frac{\sqrt{2}}{2}}\right) "" />
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<expression label="text11" exp=""\left(\fgcolor{" + (LaTeX[xColour]) + "}{\frac{\sqrt{2}}{2}},\fgcolor{" + (LaTeX[yColour]) + "}{-\frac{\sqrt{2}}{2}}\right) "" />
<element type="text" label="text11">
<show object="true" label="false"/>
<condition showObject="round(α) ≟ 315° ∨ d"/>
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