Solve trigonometric equation with exact values

A question is this type if and only if it requires solving a trigonometric equation to find exact solutions (involving surds, fractions of π, or exact angle values) in a given interval, possibly using identities or algebraic manipulation.

3 questions · Standard +0.1

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CAIE P1 2024 November Q2

2 marks Moderate -0.3

2 Find the exact solution of the equation $$\cos \frac { 1 } { 6 } \pi + \tan 2 x + \frac { \sqrt { 3 } } { 2 } = 0 \text { for } - \frac { 1 } { 4 } \pi < x < \frac { 1 } { 4 } \pi .$$

OCR MEI Paper 3 2022 June Q4

5 marks Standard +0.3

4 In this question you must show detailed reasoning.
Determine the exact solutions of the equation \(2 \cos ^ { 2 } x = 3 \sin x\) for \(0 \leqslant x \leqslant 2 \pi\).

WJEC Unit 1 2024 June Q15

7 marks Standard +0.3

The diagram shows a sketch of part of the curve with equation \(y = 2 \sin x + 3 \cos ^ { 2 } x - 3\). The curve crosses the \(x\)-axis at the points \(O , A , B\) and \(C\).
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Find the value of \(x\) at each of the points \(A , B\) and \(C\).