Double-angle and reduction formulas
Answers are for parents and teachers.
1
If sin α = 5/13 and 0 < α < π/2, find sin 2α.
120/169
2
If cos α = 2/3, find cos 2α.
−1/9
3
Compute cos² (π/8) − sin² (π/8).
√2/2
4
Compute sin 840° and tan 495°.
sin 840° = sin 120° = √3/2; tan 495° = tan 135° = −1
5
Prove sin(π − α) = sin α with an addition formula.
sin(π − α) = sin π cos α − cos π sin α = 0 · cos α − (−1) sin α = sin α.