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Wikibooks

Up to date as of January 23, 2010

From Wikibooks, the open-content textbooks collection

< Trigonometry

The principal identities in trigonometry are:

sin2θ + cos2θ = 1

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

Four trigonometric functions are 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) = cos2α − sin2α

Substituting sin2α + cos2α = 1 gives

cos(2α) = 2cos2α − 1

cos(2α) = 1 − 2sin2α

sin(3θ) = 3sinθ − 4sin3θ

cos(3θ) = 4cox3θ − 3cosθ

2sin(A)cos(B) = sin(A + B) + sin(AB)


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