Exact values of sin/cos/tan

Memorise sin/cos/tan for 0°, 30°, 45°, 60°, 90°. Higher tier requirement.

Higher tier requires exact values (in surd form) for the standard angles. Useful for GCSE and essential for A-Level.

Worked examples

sin 30 = 1/2, cos 30 = √3/2, tan 30 = 1/√3.

sin 45 = cos 45 = √2/2 = 1/√2; tan 45 = 1.

sin 60 = √3/2, cos 60 = 1/2, tan 60 = √3.

Frequently asked questions

Memorisation trick?

Triangle method: half-equilateral (30/60/90) gives 30 and 60 values; isosceles right-angled gives 45.

0 and 90?

sin 0 = 0, cos 0 = 1, tan 0 = 0. sin 90 = 1, cos 90 = 0, tan 90 undefined.