Related angles
Answers are for parents and teachers.
1
Find without a calculator: sin 135°, cos 240°, tan 330°.
√2/2, −1/2, −√3/3.
2
Simplify sin(180° + θ) + cos(90° + θ).
−sin θ + (−sin θ) = −2 sin θ.
3
Find the value of cos 690° and sin(−225°).
cos 330° = √3/2; sin 135° = √2/2.
4
Solve tan 5x = cot(x + 12°) with acute angles.
6x + 12° = 90°, so 6x = 78° and x = 13°.
5
Prove that sin 120° = cos 30° using related angles.
sin 120° = sin(180° − 60°) = sin 60° = √3/2 = cos 30°. Or sin(90° + 30°) = cos 30°.