Question

find the exact value. cos \frac{3\pi}{2}

Explanation:

Step1: Recall the unit - circle definition of cosine

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

Step2: Determine the value of \(\cos\theta\)

By the definition \(\cos\theta=x\) (where \((x,y)\) is the point on the unit - circle for angle \(\theta\)).
When \(\theta = \frac{3\pi}{2}\), \(x = 0\).

Answer:

\(0\)