Trigonometry
Core ideas
Candidates must work with sine, cosine and tangent in right-angled triangles, the sine and cosine rules in any triangle, and the area formula ½ab sin C. Also required: radians, arc length s = rθ, sector area ½r²θ, and the identities sin²θ + cos²θ = 1 and tan θ = sin θ/cos θ. Graphs of sine, cosine and tangent must be known, including amplitude and period. Solving trigonometric equations over a given interval demands finding all solutions, often using the symmetry of the graphs or a cast diagram.
Traps
- Calculator in degree mode when the question is in radians (or vice versa).
- Giving only the principal value of a trigonometric equation.
- Using the sine rule when the cosine rule is required (two sides and included angle).
- Forgetting the ambiguous case of the sine rule.
- Using degrees in arc length or sector area formulas.
Worked example
Solve 2 sin θ = 1 for 0° ≤ θ ≤ 360°. Then sin θ = 0.5, so θ = 30°. Since sine is positive in the first and second quadrants, the second solution is 180° − 30° = 150°. Solutions: 30° and 150°.
Rule of thumb
After finding a principal value, always use graph symmetry or a quadrant diagram to collect every solution inside the stated interval.