## Problem 1105

Convert the angle in degrees to radians.

-19°

Solution:-

Consider a circle of radius r. A central angle of a revolution (360°) will subtend an arc equal to the circumference of the circle. Because the circumference of the circle equal 2πr, we see that 360° = 2π radians, or 180° = π radians.

Converting form degrees to radians can be summarized as follows.

Now convert the given angle in degrees to radians. Use the formula from above to write 1 degree in radians.

-19° = -19 * 1 degree

Simplify. Remember that π 3.1416.

## Problem 1104

Determine whether the statement below is true or false.

The angular speed Ѡ of an object traveling around a circle of radius r is the angle θ (measured in radians) swept out, divide by the elapsed time t.

Solution:-

This is the definition of angular speed. The formula used to calculate angular speed is

Ѡ = .

## Problem 1103

Complete the sentence below.

An object travels around a circle of radius r with constant speed. If s is the distance traveled in time t around the circle and θ is the central angle (in radius) swept out in time t, then the linear speed of the object is v = ………and the angular speed of the object is Ѡ = ……………….

Solution:-

An object travels around a circle of radius r with constant speed. If s is the distance traveled in time t around the circle and θ is the central angle (in radius) swept out in time t, then the linear speed of the object is v = and the angular speed of the object is Ѡ = .

## Problem 1102

Complete the sentence below.

On a circle of radius r, a central angle of θ radians subtends an arc of length s = …………..; the area of the sector formed by this angle θ is A = ………………

Solution:-

On a circle of radius r, a central angle of θ radians subtends an arc of length s = r θ; the area of the sector formed by this angle θ is A = r2 θ.

## Problem 1101

Complete the sentence below.

If the radius of a circle is r and the length of the arc subtended by a central angle is also r, then the measure of the angle is 1 ……………………

Solution:-

If the radius of a circle is r and the length of the arc subtended by a central angle is also r, then the measure of the angle is 1 radian.

## Problem 1100

Complete the sentence below.

A ……………….. is a positive angle whose vertex is the center of a circle.

Solution:-

A central angle is a positive angle whose vertex is the center of a circle.

## Problem 1099

Complete the sentence below.

An angle θ is in ……………………….. , ……………………… if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.

Solution:-

An angle θ is in standard position if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.

## Problem 1098

Complete the following sentence.

If a particle has a speed of r feet per second and travels a distance d (in feet) in time (in seconds), then d = ………………..

Solution:-

d = r * t.

## Problem 1097

What is the formula for the circumference C of a circle of radius r? What is the formula for area A of a circle of radius r?

Solution:-

The formula for the circumference C of a circle of radius r is C = 2πr.

The formula for the area A of a circle of radius r is A = πr2.

## Problem 1096

Find the cosine of 90°.

Solution:-

The coordinate at 90° is (0, 1). The cosine represents the x-coordinate of the ordered pair. Therefore, the cosine of 90° is 0.