Trigonometry
Core concepts
Know the unit circle, radian–degree conversion, the six trig functions, fundamental identities (Pythagorean, reciprocal, quotient), sum/difference and double-angle formulas, and the laws of sines and cosines. Understand periodic graphs, amplitude, period, and phase shift.
Traps
- Degrees vs radians: mixing modes is a common calculator trap.
- General solutions: sin θ = 1/2 has infinitely many solutions; give all in the requested interval.
- Sign by quadrant: reference angles must be adjusted for the quadrant.
- Law of sines ambiguity (SSA): two possible triangles may exist.
- Domain restrictions: tan is undefined at π/2 + kπ.
Rule of thumb
Reduce any trig equation to a single function, then solve on [0, 2π) and add 2πk (or πk for tan) for the general solution.
Worked example
Solve 2 sin²θ − 1 = 0 on [0, 2π). Then sin²θ = 1/2, so sin θ = ±√2/2. Solutions: θ = π/4, 3π/4, 5π/4, 7π/4.