Three graphs, three identities, and an infinite number of solutions to keep track of. Most of the skill is in finding every solution inside the given interval rather than the first one your calculator hands you.
Syllabus points covered
- Sketch and use the graphs of sine, cosine and tangent, including transformations
- Use the exact values of trigonometric functions for 30°, 45° and 60°
- Use the identities sin θ / cos θ = tan θ and sin²θ + cos²θ = 1
- Use the reciprocal functions secant, cosecant and cotangent
- Solve trigonometric equations within a stated interval
Common mistakes
- Giving only the calculator's answer and missing the other solutions in the interval. Sketch the graph every time.
- Dividing through by cos x or sin x and losing a whole family of solutions. Factorise instead.
- Adjusting the interval incorrectly when the argument is 2x or (x + 30°) — widen the interval first, solve, then convert back.
- Working in degrees when the interval is given in radians, or the reverse.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Trigonometric ratios and general angles
- Trigonometric ratios and general angles — answers
- Graphs of trigonometric functions
- Graphs of trigonometric functions — answers
- Proving trigonometric identities
- Proving trigonometric identities — answers
- Mixed problems
- Mixed problems — answers
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questionsComing soon
- Mark schemeComing soon
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Additional Mathematics past papers