# Lesson 2“Sine” LanguageSolidify Understanding

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

Domain:

Range:

Positive:

Negative:

Domain:

Range:

Positive:

Negative:

Domain:

Range:

Positive:

Negative:

### 4.

Domain:

Range:

Positive:

#### d.

Negative:

Write the piecewise equation that describes each graph.

## Set

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 for a full rotation to for a full rotation.

### 7.

Calculate how high a rider will now be after passing position on the diagram.

### 8.

#### a.

Calculate the height of a rider at each of the following times , where represents the number of seconds since the rider passed position on the diagram.

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 in the diagram. Each time you should get a right triangle similar to the one in the figure.

### 9.

How did the position of the triangles you drew change between and ?

### 10.

How did the triangles you drew change between , , and ?

### 11.

How did the triangles you drew change between and ?

### 12.

Describe a relationship between the angle the hypotenuse makes with the -axis in each triangle and the angle of rotation. Use the diagram to help you think about the question. (The dotted arc shows the angle of rotation.)

## Go

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

(Assume no denominator is equal to .)