Trigonometrical Ratios of Standard Angles — Formula Sheet

sin 30° = 1/2

cos 60° = 1/2

tan 60° = √3

sin 0° = 0 and cos 0° = 1

sin 90° = 1 and cos 90° = 0

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

sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1

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

cot 30° = √3, sec 30° = 2/√3, cosec 30° = 2

cot 45° = 1, sec 45° = √2, cosec 45° = √2

If x = y = 45° or x + y = 90°, then sin x = cos y

If x = y = 45° or x + y = 90°, then tan x = cot y

If x = y = 45° or x + y = 90°, then sec x = cosec y

sin 45° = cos 45° = 1/√2

sin 30° = cos 60° = 1/2

If sin 2A = 1, then 2A = 90°

If cos 3A = 1/2, then 3A = 60°

If tan 3A = 1, then 3A = 45°

If 4sin²x° - 3 = 0, then sin x° = √3/2

For acute x, 4sin²x° - 3 = 0 gives x = 60°

If side BC is 2a and AD is drawn perpendicular to BC, then BD = a.

In right triangle ABD, AB = 2a, BD = a, and AD = √3·a.

A right-angled isosceles triangle has two equal sides AB = BC = a and one right angle of 90°.

Using Pythagoras theorem, AC = √2·a.

The Pythagorean identity is sin²A + cos²A = 1 for any angle A.

The secant-tangent identity is sec²A - tan²A = 1 for any angle A.

The cosecant-cotangent identity is cosec²A - cot²A = 1 for any angle A.

If AB = BC in a right triangle and ∠B = 90°, then ∠A = 45°.

AC = √2·a for the 45° triangle.

For any angle A, sin²A + cos²A = 1, sec²A - tan²A = 1, and cosec²A - cot²A = 1.

Also, for every value of angle θ, 1 + tan²θ = sec²θ.