Sine and Cosine with angles

Question

Find an angle θ, with 0? < θ < 360?, that has the same:

(a) Cosine as 240?

(b) Sine as 240?

Answer 1

Cosine is negative in the II and III quadrants.  The reference angle for 240 is 60.  So the other angle is in quadrant II, with reference angle 60.  The angle is 120. 

 

Sine is negative in quadrants III and IV.  The reference angle for 240 is 60.  So the other angle is in the IV quadrant, with reference angle 60. The angle is 300.

 

Ms. Gayle