# Lesson 9 Water Wheels and the Unit Circle Practice Understanding

State a negative angle of rotation that is *coterminal* with the given angle of rotation. (Coterminal angles share the same terminal side of an angle of rotation.) Sketch and label both angles.

### 1.

Given

Coterminal angle:

### 2.

Given

Coterminal angle:

### 3.

Given

Coterminal angle:

### 4.

Given

Coterminal angle:

### 5.

Given

Coterminal angle:

### 6.

What is the sum of a positive angle of rotation and the absolute value of its negative coterminal angle?

### 7.

Every angle has an infinite number of coterminal angles both positive and negative if the definition is extended to angles of rotation greater than

#### a.

Given

#### b.

Given

### 8.

Triangle

### 9.

Each point on the circle marks the end of a terminal ray in standard position. Label the measure of the angle of rotation at each position of the terminal ray. Angles will be in radians. Leave

### 10.

Use the values in #8 to write the exact coordinates of the points on the given circle. Be mindful of the numbers that are negative.

### 11.

Find the arc length,

Use your calculator to find the following values.

### 12.

### 13.

### 14.

Why are both of your answers positive?

### 15.

### 16.

### 17.

Why are both of your answers negative?

### 18.

### 19.

### 20.

In which quadrant(s) are sine and cosine both negative?

### 21.

Name an angle of rotation in radians where sine is equal to

### 22.

Name an angle of rotation where cosine is equal to

People in the 1950s and 1960s probably enjoyed music just as much as you do, but they didn’t have modern technology. They had vinyl records and phonographs. Vinyl records came in

### 23.

Calculate the angular speed of a

#### a.

#### b.

#### c.

**Angular speed** describes how fast something is turning. **Linear speed** describes how far it travels while it is turning. **Linear speed** depends on the circumference of a circle

Vinyl records were not the same size. A

### 24.

#### a.

If a fly landed on the outer edge of a

#### b.

How far if it was perched on the outside edge of a

#### c.

How far if it was perched on the outside edge of a