There are two quotient identities that can be used in right triangle trigonometry. A quotient identity defines the relations for tangent and cotangent in terms of sine and cosine.

and

Let's look at the tangent quotient identity using a familiar 30-60-90 triangle.

               

Substitute the appropriate values into the identity and simplify:







  

Let's look at the cotangent quotient identity using a familiar 45-45-90 triangle.

               

Substitute the appropriate values into the identity and simplify:







1 = 1  

The quotient identities will be used in trigonometric proofs and applications of calculus where using an identity is a more convenient form. Remember that the difference between an equation and an identity is that an identity will be true for ALL values.

Related Links: Math Trigonometry Pythagorean Identities Cofunction Identities