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:
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.
Oscar Had A Heap Of Apples 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 .