# Lesson 3More “Sine” LanguageSolidify Understanding

### 1.

The circle has been divided into equal portions. Explain the meaning of each number in the equation .

In Math II, we learned how to find the arc length of a portion of a circle when we are given the measure of the intercepted arc in degrees and the radius of the circle. We can find the fraction of the circle using , where is the measure of the intercepted arc. Then multiply the fraction of the circle times the circumference or .

Use the information in each drawing to find the length of the intercepted arc on the circle.

## Set

A right triangle has been drawn from a point on a circle centered at . The angle of rotation, , has been drawn between the initial ray and the terminal ray.

• Write the value of sine as defined in today’s lesson. (You will need to find the radius.)

• Use right angle trig to solve for angle inside the triangle.

• Use the measure of to find (the angle of rotation).

### 10.

Describe the angles of rotation that make the -values of the points be positive and the angles of rotation that make the -values be negative.

### 11.

What do you notice about the -values and the value of sine in the previous graphs?

### 12.

In the graph shown, the radius of the circle is unit. The intersections of the circle and the axes are labeled. Based on your observation in #11, what do you think the value of sine might be for the following values of ?

:

:

:

:

## Go

Make a sketch of the following problems, then solve.

### 13.

A kite is aloft at the end of a string. The string makes an angle of with the ground.

Sketch.

#### b.

How far above the ground is the kite? (Round your answer to the nearest whole number.)

### 14.

A ladder leans against a building. The top of the ladder reaches a point on the building that is above the ground. The foot of the ladder is from the building.

Sketch.

#### b.

Find to the nearest degree the measure of the angle that the ladder makes with the level ground.

### 15.

The shadow of a flagpole is long when the angle of elevation of the sun is .

Sketch.

#### b.

Find the height of the flagpole.

### 16.

The angle of depression from the top of a building to a car parked in the parking lot is . The building is high.

Sketch.

#### b.

How far from the top of the building is the car on the ground?