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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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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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