Tangent Graph - Maple Programming Help

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Tangent Graph

Main Concept

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

Explore how the unit circle can be used to construct the graph of tan($\mathbf{θ}$).



 Special values of tangent $\mathbf{θ}$ $0$ $\frac{\mathrm{\pi }}{4}$ $\frac{\mathrm{π}}{2}$ $\mathbf{tan}\left(\mathbf{θ}\right)$ $0$ $1$ Undefined $-1$ $0$

Note: The vertical lines represent vertical asymptotes as $\mathrm{tan}\left(\mathrm{θ}\right)$ is undefined at  $\mathrm{θ}=\left(\frac{n}{2}\right)\mathrm{π}$, where n is an odd integer.

Explore how the ratio of sin($\mathbf{θ}$) and cos($\mathbf{θ}$) can be used to construct the tan($\mathbf{θ}$) graph

Notice that whenever cos($\mathrm{θ}$) (blue graph) has a value of zero, tan($\theta$) has a vertical asymptote.



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