Question

The measure of angle θ is 3pi/2 . The measure of its reference angle is /, and tan θ is .

Answer 1

I know for a fact that the reference angle for 3pi/2 is pi/2 so the first one is A, and if I'm not mistaken, the second one should be undefined.

Explanation:

Answer 2

Reference angle:
`(\pi)/(2)`

`tan(\theta)=tan((3\pi)/(2))` is not defined.

Explanation:

The angle
`\theta` goes from the positive x-axis to the negative y-axis.

Therefore the reference angle can be calculated as following:

`(3\pi)/(2)-\pi=(\pi)/(2)`

We know that
`tan(\theta)`is:

`tan(\theta)=(sin(\theta))/(cos(\theta))`

If
`\theta=(3\pi)/(2)` then
`cos((3\pi)/(2))=0`, therefore
`tan((3\pi)/(2))` is not defined, because the division by 0 is not defined.