# 1.24: Cofunction Identities and Reflection

**At Grade**Created by: CK-12

**Practice**Cofunction Identities and Reflection

While toying with a triangular puzzle piece, you start practicing your math skills to see what you can find out about it. You realize one of the interior angles of the puzzle piece is , and decide to compute the trig functions associated with this angle. You immediately want to compute the cosine of the angle, but can only remember the values of your sine functions.

Is there a way to use this knowledge of sine functions to help you in your computation of the cosine function for ?

Read on, and by the end of this Concept, you'll be able to apply knowledge of the sine function to help determine the value of a cosine function.

### Watch This

### Guidance

In a right triangle, you can apply what are called "cofunction identities". These are called cofunction identities because the functions have common values. These identities are summarized below.

#### Example A

Find the value of .

**
Solution:
**
Because this angle has a reference angle of
, the answer is
.

#### Example B

Find the value of .

**
Solution:
**
Because this angle has a reference angle of
, the answer is
.

#### Example C

Find the value of .

**
Solution:
**
Because this angle has a reference angle of
, the answer is

### Vocabulary

**
Cofunction Identity:
**
A
**
cofunction identity
**
is a relationship between one trig function of an angle and another trig function of the complement of that angle.

### Guided Practice

1. Find the value of using a cofunction identity.

2. Find the value of using a cofunction identity.

3. Find the value of using a cofunction identity.

**
Solutions:
**

1. The sine of is equal to .

2. The cosine of is equal to .

3. The cosine of is equal to .

### Concept Problem Solution

Since you now know the cofunction relationships, you can use your knowledge of sine functions to help you with the cosine computation:

### Practice

- Find a value for for which is true.
- Find a value for for which is true.
- Find a value for for which is true.
- Find a value for for which is true.
- Use cofunction identities to help you write the expression as the function of an acute angle of measure less than .
- Use cofunction identities to help you write the expression as the function of an acute angle of measure less than .
- Use cofunction identities to help you write the expression as the function of an acute angle of measure less than .
- Use a right triangle to prove that .
- Use the sine and cosine cofunction identities to prove that .

### Image Attributions

## Description

## Learning Objectives

Here you'll learn about the four cofunction identities and how to apply them to solve for the values of trig functions.