Exact trig values · Year 12
In Year 12 you get fluent with: exact values in problems.
For the angles 0°, 30°, 45°, 60° and 90°, the values of sin, cos and tan can be written exactly, using surds where needed. They come from two special triangles: half a square and half an equilateral triangle.
Key facts
- sin 30° = 1/2, cos 30° = (√3)/2, tan 30° = 1/(√3) = (√3)/3.
- sin 45° = cos 45° = (√2)/2 (that is 1/(√2)), and tan 45° = 1.
- sin 60° = (√3)/2, cos 60° = 1/2, tan 60° = √3.
- sin 0° = 0, cos 0° = 1, tan 0° = 0; sin 90° = 1, cos 90° = 0 (tan 90° is undefined).
- Half-square triangle: sides 1, 1, √2. Half-equilateral triangle: sides 1, √3, 2.