# Lesson 5Maintaining Your IdentitySolidify Understanding

In the diagram, triangle is a right triangle.

• Point is any point on the circle and is described by the rectangular coordinates .

• is the length of the arc subtended by angle .

• is the radius of circle .

### 1.

is described by .

Find .

#### b.

Find to the nearest thousandth of a radian. ( decimal places)

#### c.

Find by using the formula .

#### d.

Describe point using the coordinates .

#### e.

Describe point using the radius and arc length .

### 2.

is described by .

Find .

#### b.

Find to the nearest thousandth of a radian. ( decimal places)

#### c.

Find by using the formula .

#### d.

Describe point using the coordinates .

#### e.

Describe point B using the radius and arc length .

### 3.

is described by .

Find .

#### b.

Find to the nearest thousandth of a radian. ( decimal places).

#### c.

Find by using the formula .

#### d.

Describe point using the coordinates .

#### e.

Describe point using the radius and arc length .

### 4.

is described by .

Find .

#### b.

Find to the nearest thousandth of a radian. ( decimal places).

#### c.

Find by using the formula .

#### d.

Describe point using the coordinates .

#### e.

Describe point using the radius and arc length .

## Set

The Cofunction identity states: and .

Complete the statements, using the Cofunction identity.

### 14.

Let .

#### a.

Use the Pythagorean identity to find the value of , given .

#### b.

Use the Quotient identity , the given information, and your answer in part (a) to calculate the value of .

Let .

Find given: .

Find .

Find .

### 16.

Write in a different form to see if the given identity is true.

### 17.

Perform the indicated multiplication to see if you can get the Pythagorean Identity.

### 18.

Use your work in problem #17 to prove .

### 19.

Rearrange the terms in this equation until you get the Pythagorean Identity.

## Go

Find two solutions in degrees and two solutions in radians for each equation. and . Do NOT use a calculator.

degrees:

degrees:

degrees:

degrees: