Question

evaluate the following trigonometric function at the quadrantal angle, or state that the expression is undefined. cos $\frac{3pi}{2}$

Explanation:

Step1: Recall cosine function values

The cosine function $y = \cos\theta$ represents the $x$-coordinate of a point on the unit - circle corresponding to the angle $\theta$.

Step2: Identify the position of the angle

The angle $\theta=\frac{3\pi}{2}$ in radians corresponds to a point on the unit - circle with coordinates $(0, - 1)$.

Step3: Determine the cosine value

Since $\cos\theta$ is the $x$-coordinate of the point on the unit - circle corresponding to the angle $\theta$, for $\theta=\frac{3\pi}{2}$, we have $\cos\frac{3\pi}{2}=0$.

Answer:

$0$