Cosecant identity: csc θ = 1 / sin θ
Cosecant is the reciprocal of sine, so csc θ = 1/sin θ. It is undefined wherever sin θ = 0 - at 0, π and every multiple of π. Note the mismatch students trip on: cosecant goes with sine, not cosine.
Related Reciprocal identities
Common questions
What is the csc θ = 1/sin θ identity?
Cosecant is the reciprocal of sine, so csc θ = 1/sin θ. It is undefined wherever sin θ = 0 - at 0, π and every multiple of π.
When do you use the csc θ = 1/sin θ identity?
Note the mismatch students trip on: cosecant goes with sine, not cosine.
Which identities are related to csc θ = 1/sin θ?
csc θ = 1/sin θ belongs to the Reciprocal group. The identities used alongside it most often are sec θ = 1/cos θ and cot θ = 1/tan θ.
Practise it
Reading a formula is not the same as recalling it under time pressure. The workspace drills Reciprocal 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.