Exam-Style Question on Trigonometric Equations
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 464. This question is similar to one that appeared on an A-Level paper (specimen) for 2017. The use of a calculator is allowed.
(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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