Question

evaluate the following trigonometric function at the quadrantal angle, or state that the expression is undefined.
cos\frac{\pi}{2}
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the value of cos\frac{\pi}{2} is
b. cos\frac{\pi}{2} is undefined.

Explanation:

Step1: Recall the unit circle definition

The cosine of an angle in the unit circle is the x - coordinate of the point on the unit circle corresponding to that angle. For the angle $\frac{\pi}{2}$ (or 90 degrees), the point on the unit circle is (0, 1).

Step2: Determine the value of $\cos\frac{\pi}{2}$

Since $\cos\theta=x$ (where $(x,y)$ is the point on the unit circle for angle $\theta$), when $\theta = \frac{\pi}{2}$, $x = 0$. So $\cos\frac{\pi}{2}=0$.

Answer:

A. The value of $\cos\frac{\pi}{2}$ is $0$.