Exact Trigonometric Values

This lesson covers the exact values of sin, cos, and tan for the standard angles 0°, 30°, 45°, 60°, and 90° (and their radian equivalents). These values appear throughout A-Level Mathematics — in trigonometric equations, calculus, coordinate geometry, and mechanics. You are expected to recall them without a calculator.

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Why Exact Values Matter

In many exam questions — especially "show that" and "prove" questions — you must use exact values rather than decimal approximations. Writing sin 60° = 0.866 will not earn full marks; you need sin 60° = √3/2.

Exact values also arise naturally when solving trigonometric equations, and you will use them extensively in the addition and double angle formulae covered in later lessons.

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The Standard Exact Values

Table of Exact Values