We want to see how many times is the tangent function undefined on the unit circle. We will see that two times.
Remember that:
tan(θ) = sin(θ)/cos(θ) = y/x
Where y and x are the coordinates of the point in the unit circle that defines the angle theta.
Remember that we can't divide by zero, so we have problems when x = 0.
Now, there are two points on the unit circle with that property, these points are:
(0, 1) and (0, -1)
So there are two points on the unit circle with x = 0, thus:
tan(θ) = y/x
Is undefined twice on the unit circle.
If you want to learn more about trigonometry, you can read:
https://brainly.com/question/14599603
