Exact trig values you should not calculator
Memorise 0°, 30°, 45°, 60°, 90° for sin, cos and tan.
Key formulas
Why exact?
Many papers want √3 or 1/2, not 0.866. Calculator decimals can lose method marks when exact is expected.
Triangles behind them
Half an equilateral gives 30-60. Isosceles right triangle gives 45-45.
Quick table
sin: 0,1/2,√2/2,√3/2,1. cos reverses that list. tan: 0,1/√3,1,√3, undef.
Worked example
Worked example
Problem. Without a calculator, find sin 30°, cos 45° and tan 60°.
Solution. sin 30° = 1/2. cos 45° = √2/2. tan 60° = √3.
tan60
√3 — write it, do not punch it unless asked to approximate.
Review quiz
cos 45° equals:
Practice questions
- Write exact sin60 and cos45.
- Find exact tan30 without a calculator.
Study notes
What about 15°?
Needs angle formulas; not usually required as memorised values.