Question

use the unit circle, along with the definitions of the circular functions, to find the exact values for the given functions when s = -π/2. sin(-π/2), cos(-π/2), tan(-π/2). select the correct choice below and fill in any answer boxes in your choice. a. sin(-π/2)=□ (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) b. the solution is undefined. select the correct choice below and fill in any answer boxes in your choice. a. cos(-π/2)=□ (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) b. the solution is undefined. what is the value of tan(-π/2)? a. -1 b. 1 c. 0 d. the solution is undefined

Explanation:

Step1: Recall unit - circle definitions

On the unit circle, for an angle $\theta$, $\sin\theta$ is the $y$ - coordinate of the point on the unit circle corresponding to the angle $\theta$, $\cos\theta$ is the $x$ - coordinate of the point on the unit circle corresponding to the angle $\theta$, and $\tan\theta=\frac{\sin\theta}{\cos\theta}$.

Step2: Find $\sin(-\frac{\pi}{2})$

The angle $\theta =-\frac{\pi}{2}$ corresponds to the point $(0, - 1)$ on the unit circle. So, $\sin(-\frac{\pi}{2})=-1$.

Step3: Find $\cos(-\frac{\pi}{2})$

The angle $\theta =-\frac{\pi}{2}$ corresponds to the point $(0, - 1)$ on the unit circle. So, $\cos(-\frac{\pi}{2}) = 0$.

Step4: Find $\tan(-\frac{\pi}{2})$

Since $\tan\theta=\frac{\sin\theta}{\cos\theta}$, and $\sin(-\frac{\pi}{2})=-1$, $\cos(-\frac{\pi}{2}) = 0$, then $\tan(-\frac{\pi}{2})=\frac{-1}{0}$, which is undefined.

Answer:

A. $\sin(-\frac{\pi}{2})=-1$
A. $\cos(-\frac{\pi}{2}) = 0$
D. The solution is undefined