find the exact value. cos 3π/2

Answer:

0

Explanation:

Step1: Recall cosine angle - value relationship

We know that the cosine function $y = \cos\theta$ has a unit - circle definition. The angle $\theta=\frac{3\pi}{2}$ in radians corresponds to a point on the unit circle.

Step2: Identify the $x$ - coordinate on the unit circle

The coordinates of a point on the unit circle for an angle $\theta$ are given by $(x,y)=(\cos\theta,\sin\theta)$. For $\theta = \frac{3\pi}{2}$, the point on the unit circle is $(0, - 1)$. Since $\cos\theta$ is the $x$ - coordinate of the point on the unit circle corresponding to the angle $\theta$, when $\theta=\frac{3\pi}{2}$, $\cos\frac{3\pi}{2}=0$.