Question

use the unit - circle, along with the definitions of the circular functions, to find the exact values for the given functions when s = - 2π. sin(-2π), cos(-2π), tan(-2π). select the correct choice below and fill in any answer boxes in your choice. a. sin(-2π)= (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) b. the solution is undefined.

Explanation:

Step1: Recall sine - function property

The sine function is an odd function, i.e., $\sin(-\alpha)=-\sin(\alpha)$. Here $\alpha = 2\pi$.

Step2: Evaluate $\sin(2\pi)$

On the unit - circle, for an angle $\theta = 2\pi$, the $y$ - coordinate (which is the value of $\sin\theta$) is 0. So, $\sin(2\pi)=0$.

Step3: Calculate $\sin(-2\pi)$

Since $\sin(-2\pi)=-\sin(2\pi)$ and $\sin(2\pi) = 0$, then $\sin(-2\pi)=-0 = 0$.

Answer:

A. $\sin(-2\pi)=0$