Identity library · 6 formulas
Cofunction and even/odd identities
Cofunction identities say sin and cos are the same function read from the other acute angle of a right triangle: sin θ = cos(90° − θ). The even/odd identities say which functions flip sign when the angle does: cos and sec survive, sin, tan, cot and csc change sign.
Every cofunction and even/odd identities on this site
| Formula | Name | Used for |
|---|---|---|
| sin(−θ) = −sin θ | Sine is odd | simplify, verify |
| cos(−θ) = cos θ | Cosine is even | simplify, verify |
| tan(−θ) = −tan θ | Tangent is odd | simplify, verify |
| sin θ = cos(90° − θ) | Cofunction identity for sine | simplify, evaluate, verify |
| cos θ = sin(90° − θ) | Cofunction identity for cosine | simplify, evaluate, integrate |
| tan θ = cot(90° − θ) | Cofunction identity for tangent | simplify, evaluate |
Cofunction and even/odd identities (6)
Complementary-angle pairs, and what happens to a negative angle.
| Identity | Name | proof |
|---|---|---|
| sin(−θ) = −sin θ | Sine is odd | proof |
| cos(−θ) = cos θ | Cosine is even | proof |
| tan(−θ) = −tan θ | Tangent is odd | proof |
| sin θ = cos(90° − θ) | Cofunction identity for sine | proof |
| cos θ = sin(90° − θ) | Cofunction identity for cosine | proof |
| tan θ = cot(90° − θ) | Cofunction identity for tangent | proof |
Doing something with them
- Which identity should I use? — describe an expression, get the rule.
- Verify — check a claim, see a counterexample if it is false.
- Printable cheat sheet — this family pre-selected.