Identity library · 5 formulas
Reciprocal and quotient identities
These six definitions are the translation layer: they turn tan, sec and csc into sin and cos, which is where every other identity lives. Most stalled verifications restart here — write everything in sines and cosines, then look again.
Every reciprocal and quotient identities on this site
| Formula | Name | Used for |
|---|---|---|
| tan θ = sin θ / cos θ | Quotient identity (tangent) | verify, simplify, solve |
| csc θ = 1/sin θ | Reciprocal identity (cosecant) | verify, simplify |
| sec θ = 1/cos θ | Reciprocal identity (secant) | verify, simplify, integrate |
| cot θ = 1/tan θ | Reciprocal identity (cotangent) | verify, simplify |
| cot θ = cos θ / sin θ | Quotient identity (cotangent) | verify, simplify |
Reciprocal and quotient identities (5)
csc, sec, cot as reciprocals; tan = sin/cos and cot = cos/sin.
| Identity | Name | proof |
|---|---|---|
| csc θ = 1/sin θ | Reciprocal identity (cosecant) | proof |
| sec θ = 1/cos θ | Reciprocal identity (secant) | proof |
| cot θ = 1/tan θ | Reciprocal identity (cotangent) | proof |
| tan θ = sin θ / cos θ | Quotient identity (tangent) | proof |
| cot θ = cos θ / sin θ | Quotient identity (cotangent) | 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.