## Archive for the ‘Trigonometry’ Category

## 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 = r^{2} 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 = πr^{2}.

## 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.

## Problem 1095

Explain the meaning of SOH of the mnemonic device SOH-CAH-TOA.

**Solution:-**

The mnemonic device of SOH-CAH-TOA represents the trigonometric ratios for the sine, cosine, and tangent functions. The sine of an angle is equal to the opposite side divided by the hypotenuse.