Solve trigonometric equation to find exact trigonometric ratio

A question is this type if and only if it requires using a trigonometric equation or identity to find the exact value of a trigonometric ratio (such as sin θ, cos θ, or tan θ) rather than finding angle values, typically involving algebraic manipulation and possibly Pythagorean identities.

2 questions · Standard +0.8

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OCR H240/03 Q3

4 marks Standard +0.8

3 In this question you must show detailed reasoning. Given that \(5 \sin 2 x = 3 \cos x\), where \(0 ^ { \circ } < x < 90 ^ { \circ }\), find the exact value of \(\sin x\).

AQA Paper 2 2024 June Q6

6 marks Standard +0.8

6 It is given that $$( 2 \sin \theta + 3 \cos \theta ) ^ { 2 } + ( 6 \sin \theta - \cos \theta ) ^ { 2 } = 30$$ and that \(\theta\) is obtuse. Find the exact value of \(\sin \theta\). Fully justify your answer.