Co-function Identities

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)

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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)

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

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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

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