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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(&pi/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

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

More Lessons for Trigonometry

Math Worksheets

In this lesson, we will look at 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°

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(&pi/6)

Find a possible acute angle solution

cos(2θ + 16°) = sin(θ + 11°)

Find a possible acute angle solution

cot(θ) = tan(θ + π/6)

Example:

If sin 72° = 0.9511

find cos 18°

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

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

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

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