← Additional Mathematics syllabus

SingaporeAdditional Mathematics

Trigonometry and Identities

3 dot points across 3 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we solve a trigonometric equation and find all the angles in a given range?

Solve simple trigonometric equations within a stated range using the basic angle and the quadrant rule
A focused answer to the N(A)-Level Additional Mathematics outcome on trigonometric equations. Find the basic angle, use the quadrant sign rule to locate all solutions, and list every angle within a stated range.
8 min answer →

What are the basic trigonometric identities, and how do we use them to simplify or prove expressions?

Use the identities tan equals sin over cos and sin squared plus cos squared equals one to simplify expressions and prove simple results
A focused answer to the N(A)-Level Additional Mathematics outcome on trigonometric identities. The quotient identity, the Pythagorean identity, and how to use them to simplify expressions and prove simple results.
8 min answer →

How do the sine, cosine and tangent ratios extend beyond right-angled triangles using the unit circle?

Define sine, cosine and tangent for any angle using the unit circle, and find exact values and signs in each quadrant
A focused answer to the N(A)-Level Additional Mathematics outcome on trigonometric ratios. The unit-circle definitions of sine, cosine and tangent, the sign of each ratio in the four quadrants, and exact values for standard angles.
8 min answer →