Trigonometry/Trigonometric Formula Reference

Current revision (unreviewed)

The principal identities in trigonometry are:

$sin 2 θ + cos 2 θ = 1$

$\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}$

Four trigonometric functions are $2π$ periodic:

$sinθ = sin(θ + 2π)$

$cosθ = cos(θ + 2π)$

$cscθ = csc(θ + 2π)$

$secθ = sec(θ + 2π)$

Two trigonometric functions are $π$ periodic:

$tanθ = tan(θ + π)$

$cotθ = cot(θ + π)$

Formulas involving sums of angles are as follows:

$sin(α + β) = sinαcosβ + cosαsinβ$

$cos(α + β) = cosαcosβ - sinαsinβ$

Substituting $β = α$ gives the double angle formulae

$sin(2α) = 2sin(α)cos(α)$

$cos(2α) = cos 2 α - sin 2 α$

Substituting $sin 2 α + cos 2 α = 1$ gives

$cos(2α) = 2cos 2 α - 1$

$cos(2α) = 1 - 2sin 2 α$

$sin(3θ) = 3 s i n θ - 4 s i n 3 θ$

$cos(3θ) = 4 c o x 3 θ - 3 c o s θ$

$2sin(A) c o s (B) = s i n (A + B) + s i n (A - B)$