Trigonometric Functions — Formula Sheet

1 degree = (1/360)th of a revolution

1 degree = 60 minutes; 1 minute = 60 seconds

1 complete revolution = 2π radian

θ = l/r

l = rθ

We define cos x = a and sin x = b

cos²x + sin²x = 1

sin(2nπ + x) = sin x

cos(2nπ + x) = cos x

sin x = 0 implies x = nπ

sin x is positive for 0 < x < π and negative for π < x < 2π

cos x is positive for 0 < x < π/2 and 3π/2 < x < 2π; negative for π/2 < x < 3π/2

tan x is positive in Quadrants I and III; negative in Quadrants II and IV

cot x is positive in Quadrants I and III; negative in Quadrants II and IV

cosec x is positive in Quadrants I and II; negative in Quadrants III and IV

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

sin 90° = 1, cos 90° = 0, tan 90° is not defined

sin π = 0, cos π = -1, tan π = 0

For every point on the unit circle, cos²x + sin²x = 1.

cosec x = 1/sin x, sec x = 1/cos x, tan x = sin x/cos x, cot x = cos x/sin x.

cos x = 0 implies x = (2n + 1)π/2, where n is any integer.

tan(x + y) = (tan x + tan y)/(1 − tan x tan y), provided none of x, y, or x + y is an odd multiple of π/2.

1 degree = 1/360 of a revolution.

cos^2 x + sin^2 x = 1 for every x.

In a circle of radius r, an arc of length l subtends an angle θ at the centre, where l = rθ.