Trigonometry — A-Level Mathematics Revision
Revise Trigonometry for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Exponentials & LogarithmsWhat is Trigonometry?
A-Level Trigonometry expands on GCSE concepts to include the study of trigonometric functions, their graphs, and identities. Key topics include solving trigonometric equations, proving identities, and understanding the relationships between sine, cosine, and tangent, as well as their reciprocal functions.
Board notes: All A-Level Maths boards (AQA, Edexcel, OCR) cover trigonometry extensively. The specific identities and the complexity of the equations to be solved can vary, but the core principles are consistent across all boards.
Step-by-step explanationWorked example
Solve the equation 2sin²x - cosx - 1 = 0 for 0° ≤ x ≤ 360°. First, use the identity sin²x = 1 - cos²x to get an equation in terms of cosx: 2(1 - cos²x) - cosx - 1 = 0. This simplifies to 2cos²x + cosx - 1 = 0. Factoring gives (2cosx - 1)(cosx + 1) = 0. So, cosx = 1/2 or cosx = -1. For cosx = 1/2, x = 60° and x = 300°. For cosx = -1, x = 180°. The solutions are x = 60°, 180°, 300°.
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Common mistakes
- 1Forgetting to find all solutions to a trigonometric equation within a given range. The periodic nature of trigonometric functions means there are often multiple solutions.
- 2Confusing radians and degrees. Calculators must be in the correct mode, and it's essential to know when to use each unit.
- 3Incorrectly applying trigonometric identities. For example, confusing sin²x + cos²x = 1 with other identities like tan²x + 1 = sec²x.
Trigonometry exam questions
Exam-style questions for Trigonometry with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Trigonometry
Core concept
A-Level Trigonometry expands on GCSE concepts to include the study of trigonometric functions, their graphs, and identities. Key topics include solving trigonometric equations, proving identities, and…
Frequently asked questions
What are the reciprocal trigonometric functions?
The reciprocal trigonometric functions are cosecant (cosec), secant (sec), and cotangent (cot). They are the reciprocals of sine, cosine, and tangent, respectively.
How do I prove a trigonometric identity?
To prove a trigonometric identity, you should start with one side of the identity and use known identities and algebraic manipulation to show that it is equivalent to the other side.