Sine Graph - Maple 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.



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

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.

 $r$ =   



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