# Co-function Identities

Related Topics:
More Lessons for Trigonometry
Math Worksheets

In this lesson, we will look at co-function identities.

What are the Co-function Identities?
A function f is cofunction of a function g if f(A) = g(B) when A and B are complementary angles.

sin A = cos(90° - A)
cos A = sin(90° - A)
sin A = cos B, if A + B = 90°

sec A = csc(90° - A)
csc A = sec(90° - A)
sec A = csc B, if A + B = 90°

tan A = cot(90° - A)
cot A = tan(90° - A)
tan A = cot B, if A + B = 90°

Cofunction Identities
This video explains the cofunction identities and how to determine cofunctions given a function value.
What is a cofunction.
Finding the cofunction.
Using the cofunction relationship

Examples:
Write each function in terms of its cofunction.

1. sin(18°)
2. tan(65°)
3. csc(84°)

Write each function in terms of its cofunction.

1. cos(π/4)
2. cot(π/3)
3. sec(π/6)

How to use cofunction identities to solve trigonometric equations? Examples:
Find a possible acute angle solution
cos(2θ + 16°) = sin(θ + 11°)

Find a possible acute angle solution
cot(θ) = tan(θ + π/6)

Cofunctions
Example:
If sin 72° = 0.9511
find cos 18°

Cofunction Identities in Trigonometry
The cofunction identities state that
The value of any trigonometric function at x is equal to the value of the cofunction at (π/2 - x).

cos(π/2 - x) = sin x
sin(π/2 - x) = cos x
tan(π/2 - x) = cot x
cot(π/2 - x) = tan x
sec(π/2 - x) = csc x
csc(π/2 - x) = sec x

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 