Question

I don't know how to solve this?

Answer 1

a. `alpha` = 150

b. `alpha` = 330

Explanation:

You can look at the problem this way:

`sin 30 = 1/2`

`cos 30 = 1/2`

The question is basically asking you that what other value of `alpha` will yield the same result?

You can recall from the symmetry of the unit circle that the following results always hold:

`sin theta = sin (180-theta)`

`cos theta = cos (360-theta)`

This is because sine is always positive in the first and the second quadrant while cosine is always positive in the first and the fourth quadrant. Hence, we can solve the given problem:

`sin 30 = sin(180-30) = sin 150`

so `alpha` = 150 (for part a)

`cos 30 = cos (360-30) = cos(330)`

so `alpha` = 330 (for part b)

Hope this helps!