Tangent quotient identity: tan θ = sin θ / cos θ
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.
Related Quotient identities
Common questions
What is the tan θ = sin θ/cos θ identity?
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.
Which identities are related to tan θ = sin θ/cos θ?
tan θ = sin θ/cos θ belongs to the Quotient group. The identities used alongside it most often are cot θ = cos θ/sin θ.
Practise it
Reading a formula is not the same as recalling it under time pressure. The workspace drills Quotient questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.
Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.