Trigonify

Topics · 3 identities

Even/Odd

Parity rules that flip or keep the sign when the angle is negated.

Sine is odd: sin(−θ) = −sin θ

sin⁡(−θ)=−sin⁡θ\sin(-\theta) = -\sin\theta

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.

Open identity

Cosine is even: cos(−θ) = cos θ

cos⁡(−θ)=cos⁡θ\cos(-\theta) = \cos\theta

Cosine is an even function: cos(−θ) = cos θ, so the sign of the angle makes no difference. Its graph is symmetric about the vertical axis. Cosine being even while sine is odd is precisely why the sum and difference formulas have the ± / ∓ pairings they do.

Open identity

Tangent is odd: tan(−θ) = −tan θ

tan⁡(−θ)=−tan⁡θ\tan(-\theta) = -\tan\theta

Tangent is odd, so tan(−θ) = −tan θ. It follows directly from sine being odd and cosine being even: the sign in the numerator flips and the denominator does not.

Open identity