Trigonify

Topics · 2 identities

Quotient

Tangent and cotangent written as quotients of sine and cosine.

Tangent quotient identity: tan θ = sin θ / cos θ

tan⁡θ=sin⁡θcos⁡θ\tan\theta = \dfrac{\sin\theta}{\cos\theta}

Tangent is the quotient of sine and cosine: tan θ = sin θ / cos θ. This is the identity that turns a mixed expression into one written purely in sines and cosines, which is almost always the first move when simplifying or proving an identity.

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Cotangent quotient identity: cot θ = cos θ / sin θ

cot⁡θ=cos⁡θsin⁡θ\cot\theta = \dfrac{\cos\theta}{\sin\theta}

Cotangent is cosine over sine: cot θ = cos θ / sin θ. Together with tan θ = sin θ / cos θ it lets you rewrite any expression in sines and cosines alone - the standard opening move for an identity proof.

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