Let denote an angle.

**Definition:** The *tangent* of , denoted
is

**Definition:** The *secant* of , denoted
is

**Definition:** The *cosecant* of , denoted
is

We summarize information about the domain and range of the six trig functions:

- : Domain equals . Range equals [-1,1].
- : Domain equals . Range equals [-1,1].
- : Domain equals . Range equals .
- : Domain equals . Range equals .
- : Domain equals . Range equals .
- : Domain equals . Range equals .

Using the alternate definition of sine and cosine as ratios of sides of right triangles, we can give alternate definitions of tangent, secant, cosecant, and cotangent.

- .
- .
- .
- .

**O**scar **H**ad **A** **H**eap **O**f **A**pples
is a mnemonic to remember that , ,
and .

Starting with the known trigonometric identity we can derive two more identities by dividing both sides of this equation by and by .

Wed Apr 21 08:17:28 EDT 1999