Question

use the unit circle to find the value of sin(3π/2) and even or odd trigonometric functions to find the value of sin(-3π/2). select the correct choice below and fill in any answer boxes within your choice. a. sin(3π/2) = (type an exact answer, using radicals as needed. simplify your answer. rationalize the denominator.) b. the expression is undefined.

Explanation:

Step1: Locate angle on unit - circle

The angle $\theta=\frac{3\pi}{2}$ corresponds to the point $(0, - 1)$ on the unit - circle. The sine of an angle $\theta$ in the unit - circle is given by the $y$ - coordinate of the point where the terminal side of the angle intersects the unit - circle. So, $\sin\frac{3\pi}{2}=-1$.

Step2: Use property of odd trigonometric function

The sine function is an odd function, i.e., $\sin(-\theta)=-\sin\theta$. For $\theta = \frac{3\pi}{2}$, we have $\sin(-\frac{3\pi}{2})=-\sin\frac{3\pi}{2}$. Since $\sin\frac{3\pi}{2}=-1$, then $\sin(-\frac{3\pi}{2})=-(-1) = 1$.

Answer:

A. $\sin\frac{3\pi}{2}=-1$; $\sin(-\frac{3\pi}{2}) = 1$