Question

find the exact values of the six trigonometric functions of the given angle. if any are not defined, say
ot defined.\. do not use a calculator. what is the value of sin(7π/2)? select the correct choice and, if necessary, fill in the answer box to complete your choice. a. sin(7π/2)= (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) b. the function is not defined.

Explanation:

Step1: Rewrite the angle

Rewrite $\frac{7\pi}{2}$ as $3\pi+\frac{\pi}{2}$. So, $\sin\frac{7\pi}{2}=\sin(3\pi + \frac{\pi}{2})$.

Step2: Use the angle - addition formula for sine

The formula $\sin(A + B)=\sin A\cos B+\cos A\sin B$. Here $A = 3\pi$ and $B=\frac{\pi}{2}$. We know that $\sin(3\pi)=0$ and $\cos(3\pi)= - 1$, $\sin\frac{\pi}{2}=1$ and $\cos\frac{\pi}{2}=0$. Then $\sin(3\pi+\frac{\pi}{2})=\sin(3\pi)\cos\frac{\pi}{2}+\cos(3\pi)\sin\frac{\pi}{2}=0\times0+( - 1)\times1=-1$.

Answer:

-1