Sine is odd: sin(−θ) = −sin θ
Sine is an odd function, so flipping the sign of the angle flips the sign of the value: sin(−θ) = −sin θ. Its graph has rotational symmetry about the origin. This is what lets you fold negative angles out of an expression before applying any other identity.
Related Even/Odd identities
Common questions
What is the Sine is odd identity?
Sine is an odd function, so flipping the sign of the angle flips the sign of the value: sin(−θ) = −sin θ. Its graph has rotational symmetry about the origin.
When do you use the Sine is odd identity?
This is what lets you fold negative angles out of an expression before applying any other identity.
Which identities are related to Sine is odd?
Sine is odd belongs to the Even/Odd group. The identities used alongside it most often are Cosine is even and Tangent is odd.
Practise it
Reading a formula is not the same as recalling it under time pressure. The workspace drills Even/Odd 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.