# 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

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

#### Example B

Find the value of

**Solution:** Because this angle has a reference angle of

#### Example C

Find the value of

**Solution:** Because this angle has a reference angle of

### 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

2. Find the value of

3. Find the value of

**Solutions:**

1. The sine of

2. The cosine of

3. The cosine of

### 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
θ for whichsinθ=cos15∘ is true. - Find a value for
θ for whichcosθ=sin55∘ is true. - Find a value for
θ for whichtanθ=cot80∘ is true. - Find a value for
θ for whichcotθ=tan30∘ is true. - Use cofunction identities to help you write the expression
tan255∘ as the function of an acute angle of measure less than45∘ . - Use cofunction identities to help you write the expression
sin120∘ as the function of an acute angle of measure less than45∘ . - Use cofunction identities to help you write the expression
cos310∘ as the function of an acute angle of measure less than45∘ . - Use cofunction identities to help you write the expression
cot260∘ as the function of an acute angle of measure less than45∘ . - Use cofunction identities to help you write the expression
cos280∘ as the function of an acute angle of measure less than45∘ . - Use cofunction identities to help you write the expression
tan60∘ as the function of an acute angle of measure less than45∘ . - Use cofunction identities to help you write the expression
sin100∘ as the function of an acute angle of measure less than45∘ . - Use cofunction identities to help you write the expression
cos70∘ as the function of an acute angle of measure less than45∘ . - Use cofunction identities to help you write the expression
cot240∘ as the function of an acute angle of measure less than45∘ . - Use a right triangle to prove that
sinθ=cos(90∘−θ) . - Use the sine and cosine cofunction identities to prove that
tan(90∘−θ)=cotθ .

### Image Attributions

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