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