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SingaporeAdditional Mathematics

Trigonometry and Identities

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do the addition and double angle formulae let us expand and simplify trigonometric expressions of combined angles?

Apply the addition formulae for sine, cosine and tangent and the double angle formulae to expand, simplify and evaluate trigonometric expressions
A focused answer to the O-Level A-Maths outcome on compound and double angles. The addition formulae for sine, cosine and tangent, the double angle formulae, and using them to expand, simplify and find exact values.
9 min answer →

How does the R-formula combine a sine and a cosine term into one, and what does it tell us about maximum and minimum values?

Express a sine plus cosine as a single R sine or R cosine function and use it to find maximum and minimum values and to solve equations
A focused answer to the O-Level A-Maths outcome on the R-formula. Writing a cosine plus sine as a single R cosine or R sine, finding R and the angle, and using the form for maxima, minima and equations.
9 min answer →

How do we find all solutions of a trigonometric equation within a given range?

Solve trigonometric equations within a stated interval, finding the basic angle and using symmetry to obtain every solution
A focused answer to the O-Level A-Maths outcome on solving trigonometric equations. Finding the basic angle, using quadrant symmetry to list every solution in range, and handling identity-reducible equations.
9 min answer →

How do we use the Pythagorean and reciprocal identities to simplify expressions and prove trigonometric statements?

State and use the Pythagorean, reciprocal and quotient identities to simplify expressions and prove trigonometric identities
A focused answer to the O-Level A-Maths outcome on trigonometric identities. The Pythagorean, reciprocal and quotient identities, and a reliable strategy for proving identities by working one side.
9 min answer →

How do the unit circle and reference angles extend the trigonometric ratios to any angle?

Define sine, cosine and tangent for any angle using the unit circle, determine signs by quadrant, and use reference angles and special angles
A focused answer to the O-Level A-Maths outcome on trigonometric ratios. The unit-circle definitions, the signs of the ratios by quadrant, reference angles, and the exact values of special angles.
9 min answer →