Find an angle θ with 0∘<θ<360∘

Question

Find an angle  with  that has the same:

Sine as :  = ____ degrees

Cosine as :  = ___ degrees

Answer 1

Recall that sin θ is symmetric over the y-axis and cos θ is symmetric over the x-axis.

This means that if you reflect a point (cos θ, sin θ) over the y-axis, the value of sin θ will not change.

If we reflect the angle of 190° over the y-axis we get 350°

If we reflect the angle of 190° over the x-axis we get 170°

Therefore the answers are 350° and 170°.