Question

find the exact value.

cos\frac{3\pi}{2}

Explanation:

Step1: Use the unit - circle definition

The cosine of an angle \(\theta\) in the unit - circle is given by the \(x\) - coordinate of the point on the unit - circle corresponding to the angle \(\theta\).
For \(\theta=\frac{3\pi}{2}\), the point on the unit - circle is \((0, - 1)\).

Step2: Determine the cosine value

Since \(\cos\theta=x\) (from the unit - circle definition \((x,y)=(\cos\theta,\sin\theta)\)), when \(\theta = \frac{3\pi}{2}\), \(x = 0\).

Answer:

\(0\)