Trigonometry

Topic overview

P3 trigonometry questions often require switching back and forth between identity manipulation, quadrant determination and the specified interval. First unify the functions or angles, then deal with the solution set.

Key concepts

Common tools include product-to-sum and sum-to-product formulae, double-angle formulae and $R\cos(x-\alpha)$ . After solving the equation you must list all solutions according to the interval given in the question, and check the denominator restrictions in the original expression.

Key points

◆First mark the angle unit
◆Inverse trigonometric functions give only the principal value
◆Complete solutions using quadrants rather than blindly pressing the calculator

Worked examples

Try each example yourself before checking the explanation.

1Product-to-sum formulae

Find $\int_0^{\pi/6}4\cos x\cos2x\,dx$ .

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