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. sin(-π), cos(-π), tan(-π) select the correct choice below and fill in any answer boxes in your choice. a. sin(-π)= (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) b. the solution is undefined.

Explanation:

Step1: Recall unit - circle properties

On the unit circle, for an angle $\theta$, the coordinates of the corresponding point are $(\cos\theta,\sin\theta)$. The angle $\theta =-\pi$ is equivalent to an angle of $\pi$ (since angles are periodic with period $2\pi$). The point on the unit - circle corresponding to the angle $\theta=\pi$ is $(- 1,0)$.

Step2: Find $\sin(-\pi)$

By the definition of the sine function on the unit circle, $\sin\theta$ is the $y$ - coordinate of the point on the unit circle corresponding to the angle $\theta$. For $\theta =-\pi$ (or $\pi$), the $y$ - coordinate of the corresponding point $(-1,0)$ is $0$. So, $\sin(-\pi)=0$.

Step3: Find $\cos(-\pi)$

By the definition of the cosine function on the unit circle, $\cos\theta$ is the $x$ - coordinate of the point on the unit circle corresponding to the angle $\theta$. For $\theta =-\pi$ (or $\pi$), the $x$ - coordinate of the corresponding point $(-1,0)$ is $-1$. So, $\cos(-\pi)=-1$.

Step4: Find $\tan(-\pi)$

Recall that $\tan\theta=\frac{\sin\theta}{\cos\theta}$. Substituting $\sin(-\pi) = 0$ and $\cos(-\pi)=-1$ into the formula for the tangent function, we get $\tan(-\pi)=\frac{\sin(-\pi)}{\cos(-\pi)}=\frac{0}{-1}=0$.

Answer:

A. $\sin(-\pi)=0$
A. $\cos(-\pi)=-1$
A. $\tan(-\pi)=0$