What is one example of an odd trigonometric function? Show that your function meet the criteria for an odd function.

Answer 1

One example of an odd trigonometric function is the tangent function, denoted as $\tan(x)$. The tangent function is defined as the ratio of the sine function to the cosine function, $\tan(x) = \frac{\sin(x)}{\cos(x)}$.

To show that the tangent function is odd, we need to verify that $\tan(-x) = -\tan(x)$ for all $x$.

Using the definition of the tangent function, we have:

$$\tan(-x) = \frac{\sin(-x)}{\cos(-x)} = \frac{-\sin(x)}{\cos(x)} = -\frac{\sin(x)}{\cos(x)} = -\tan(x)$$

Since $\tan(-x) = -\tan(x)$ for all $x$, the tangent function is odd.