Trigonometric Functions and Identities
Core concepts
Know the Pythagorean, double-angle, and sum-to-product identities, the graphs of sine, cosine, and tangent, and how to solve trigonometric equations over a specified interval. Understand radians, amplitude, period, and phase shift.
Traps
- Losing solutions by dividing by a trigonometric factor; instead factor and consider each case.
- Forgetting to add the period when general solutions are required.
- Sign errors when using double-angle identities.
- Mixing degrees and radians in calculus contexts.
Worked example
Solve 2sin^2 x - sin x -1=0 for 0<=x<2pi. Factor: (2sin x+1)(sin x-1)=0, so sin x=-1/2 or sin x=1. The solutions are x=7pi/6, 11pi/6, and pi/2.
Rule of thumb
When solving trigonometric equations, factor rather than divide, and always check the required interval for all solutions.