Find exactly: cos 150˚ + sin 225˚?

Question

Find exactly: cos 150˚ + sin 225˚

Answer 1

150°: reference angle is 30° (180° - 30°), quadrant is 2, cos is negative:

cos 150° = -cos 30° = -√3/2

225°: reference angle is 45° (180° + 45°), quadrant is 3, sin is negative:

sin 225° = -sin 45° = -√2/2

cos 150˚ + sin 225˚ = (-√3 - √2)/2 = -(√3 +√2)/2

Answer 2

cos 150=-cos 30=-√3/2
sin 225=-sin 45=-√2/2
cos 150+sin 225=-(√3+√2)/2