Find all angles

Question

1.Determine the reference angle of 225°

2.Fund the exact value of cos225°

3.Find all angles in 0° and 180° for which sinØ = (sqrt3)/2

Answer 1

The reference angle is 45° as shown in the sketch. Since cos(45°) = √2/2, cos(225°) = √2/2 BUT we need to adjust the sign for the corresponding quadrant. In Q3 (where 225° is), cosine is negative, therefore cos(225°) = -√2/2.

sin(60°) = √3/2 but there is also an angle in Q2 that has the same reference angle like this:

This angle, which is 180° - 60° = 120° and the sine in Q2 is positive so sin(120°) = √3/2.