Step-by-step explanation:
15. If A and B are complementary angles, then sin A = cos B and cos A = sin B.
So if sin A = m, then cos B = m.
16. If sin A = cos B, or cos A = sin B, and A and B are acute, then A and B are complementary.
a. cos 60° = sin θ
60° + θ = 90°
θ = 30°
b. sin 71° = cos θ
71° + θ = 90°
θ = 19°
c. sin θ = cos (θ + 20°)
θ + θ + 20° = 90°
2θ = 70°
θ = 35°
d. sin (θ − 60°) = cos θ
θ + θ − 60° = 90°
2θ = 150°
θ = 75°
