Question

evaluate the function $f(x)=-\sin x$ at $x = \frac{3\pi}{2}$. (1 point)
$(\frac{3\pi}{2},\square)$
check answer remaining attempts : 3

Explanation:

Step1: Substitute \( x = \frac{3\pi}{2} \) into the function

\( f(\frac{3\pi}{2})=-\sin(\frac{3\pi}{2}) \)

Step2: Evaluate \( \sin(\frac{3\pi}{2}) \)

We know that \( \sin(\frac{3\pi}{2})=- 1 \) (from the unit - circle definition of sine function: for an angle \( \theta=\frac{3\pi}{2} \), the \( y \) - coordinate (which is equal to \( \sin\theta \)) is \( - 1 \))

Step3: Calculate \( f(\frac{3\pi}{2}) \)

Substitute \( \sin(\frac{3\pi}{2})=-1 \) into \( f(\frac{3\pi}{2})=-\sin(\frac{3\pi}{2}) \). Then \( f(\frac{3\pi}{2})=-(-1) \)

Answer:

\(1\)