Cosine Graph - Maple Programming Help

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Cosine Graph

Main Concept

The cosine function is one of the three primary trigonometric functions. In a right triangle, the cosine is the ratio between the length of the side adjacent to the angle and the length of the hypotenuse.

Explore by rotating the hypotenuse about the circle's center. By calculating the ratio adjacent/hypotenuse for different values of $\theta$, we can construct the graph of $\mathrm{cos}\left(\mathrm{θ}\right)$. Change the value of r with the slider and notice that this ratio is not affected.

 Special values of cosine $\mathbf{θ}$ $0$ $\frac{\mathrm{\pi }}{2}$ $\mathrm{π}$ $\mathbf{cos}\left(\mathbf{θ}\right)$ $1$ $0$ $-1$ $0$ $1$

 Notice the pattern $\mathbf{θ}$ $0$ $\frac{\mathrm{\pi }}{6}$ $\frac{\mathrm{π}}{4}$ $\frac{\mathrm{π}}{3}$ $\frac{\mathrm{π}}{2}$ $\mathbf{cos}\left(\mathbf{θ}\right)$ $\frac{\sqrt{4}}{2}$ $\frac{\sqrt{3}}{2}$ $\frac{\sqrt{2}}{2}$ $\frac{\sqrt{1}}{2}$ $\frac{\sqrt{0}}{2}$

$r$ =



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