Exact values
A standard method from Trigonometry: the steps and worked examples.
Steps
| θ | 30° | 45° | 60° |
|---|---|---|---|
| sin θ | 1/2 | √2/2 | √3/2 |
| cos θ | √3/2 | √2/2 | 1/2 |
| tan θ | √3/3 | 1 | √3 |
Build them from half an equilateral triangle (sides 1, √3, 2) and half a square (sides 1, 1, √2), rather than memorising.
Worked examples
Example 1: Exact value of sin 60° cos 30° − tan 45°
= (√3/2)(√3/2) − 1 = 3/4 − 1 = −1/4.
For the whole topic, read Trigonometry: key points, common mistakes and how the DSE tests it.