# Exam-Style Questions on Trigonometric Equations

## Problems on Trigonometric Equations adapted from questions set in previous Mathematics exams.

### 1.

A-Level

(a) Solve the following trigonometric equation for $$–360° \lt x \lt 360°$$:

$$5 \sin^2 x + 2\sin x + 3 = 7 \cos^2 x$$

giving your answers to the nearest integer.

(b) Hence find the smallest positive solution of the equation

$$5 \sin^2(3\theta + 20°) + 2\sin (3\theta + 20°) + 3 = 7 \cos^2 (3\theta + 20°)$$

giving your answer to 2 decimal places.

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