Sine Graph - Maple Programming Help

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Sine Graph

Main Concept

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

 

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

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

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

$r$ =





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