Trigonometry
Core content
Candidates need right-triangle ratios, the unit circle, degree-radian conversion, reference angles, and the graphs of sine, cosine, and tangent. Know amplitude, period, phase shift, and vertical shift. Use Pythagorean identities, reciprocal identities, and angle-sum formulas where appropriate. Solve trigonometric equations, evaluate inverse trigonometric functions with correct domains, and apply the law of sines and law of cosines to triangles. Bearings and periodic modelling are common applications.
Trap watch
Check the calculator mode before evaluating trigonometric functions. Inverse sine and cosine have restricted ranges, so a calculator gives only a principal value; other solutions may exist in the required interval. In the ambiguous SSA case, two triangles, one triangle, or none may be possible. Signs depend on the quadrant, so sketch the unit circle rather than relying on memory. The tangent function has period pi, not 2pi. Do not cancel trigonometric expressions unless the factor is never zero on the domain.
Worked example
Solve 2 sin x = 1 for 0 <= x < 2pi. Then sin x = 1/2. The reference angle is pi/6, and sine is positive in quadrants I and II, so x = pi/6 or x = 5pi/6. No other solutions lie in the interval.
Rule of thumb: sketch the unit circle, mark the reference angle, then use quadrant signs to list all solutions in the stated interval.