Exact Trigonometric Values
Grade 5Why exact values matter
Some GCSE questions say "without using a calculator" or award marks for an exact answer like √3/2. You need to know the trig values for five key angles by heart.
The values to know
sin 0° = 0, sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2, sin 90° = 1.
cos 0° = 1, cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2, cos 90° = 0.
tan 0° = 0, tan 30° = 1/√3 (= √3/3), tan 45° = 1, tan 60° = √3, tan 90° = undefined.
Notice sin and cos swap as the angle goes from 30° to 60°. And tan 45° = 1 is a dead-easy anchor. Learn those three first, fill in the rest from the pattern.
Worked example
EXAMPLE
Without a calculator, find the exact value of sin 60° × cos 30°.
sin 60° = √3/2. cos 30° = √3/2. Product = (√3/2) × (√3/2) = 3/4. Answer = 3/4.
