# Lesson 2 “Sine” Language Solidify Understanding

For each graph, identify the domain and range. Then write the interval(s) where

### 1.

#### a.

Domain:

#### b.

Range:

#### c.

Positive:

#### d.

Negative:

### 2.

#### a.

Domain:

#### b.

Range:

#### c.

Positive:

#### d.

Negative:

### 3.

#### a.

Domain:

#### b.

Range:

#### c.

Positive:

#### d.

Negative:

### 4.

#### a.

Domain:

#### b.

Range:

#### c.

Positive:

#### d.

Negative:

Write the piecewise equation that describes each graph.

### 5.

### 6.

Recall the following facts from the lesson done in class:

The Ferris wheel has a radius of

. The center of the Ferris wheel is

above the ground.

Due to a safety concern, the management of the amusement park decides to slow the rotation of the Ferris wheel from

### 7.

Calculate how high a rider will now be

### 8.

#### a.

Calculate the height of a rider at each of the following times

Elapsed time since passing position | Calculations | Height of the rider (in feet) |
---|---|---|

#### b.

Plot the position you calculated on the diagram. Connect the center of the circle to the point you plotted. Then draw a vertical line from the plotted point on the Ferris wheel to the line segment

### 9.

How did the position of the triangles you drew change between

### 10.

How did the triangles you drew change between

### 11.

How did the triangles you drew change between

### 12.

Describe a relationship between the angle

Perform the indicated operation. Divide out all common factors in your answers.

**(Assume no denominator is equal to ****.)**