Cosine Graph - Maple Help

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.

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

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.

 $r$ =   

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