Chapter 6, Problem 1RCC

a.

To determine

Explain type of angle.

Answer to Problem 1RCC

If the rotation is counter clockwise, the angle considered positive, and if the rotation is clockwise, the angle is considered negative.

Explanation of Solution

Given information:

Explain a positive and negative angle.

Calculation:

An angle $AOB$ consists of two rays $R_{1}and{R}_2$ with a common vertex. The measure of an angleis the measure of the rotation of the ray $R_{1}onto{R}_2$

  

Hence, if the rotation is counter clockwise, the angle considered positive, and if the rotation is clockwise, the angle is considered negative.

b.

To determine

Describe measurement.

Answer to Problem 1RCC

By rotating the initial side $\frac{1}{360}$ of a complete revolution.

Explanation of Solution

Given information:

Explain an angle of measure $\text{1}$ degree .

Calculation:

Consider the figure below,

  

Hence, an angle of measure $\text{1}$ degree is formed by rotating the initial side $\frac{1}{360}$ of a complete revolution.

c.

To determine

Describe measurement.

Answer to Problem 1RCC

An angle of measure $\text{1}$ radian is subtended by the arc of length $\text{1}$ along the unit circle.

Explanation of Solution

Given information:

Explain an angle of measure $\text{1}$ radian .

Calculation:

The measure of the angle in radians is the length of the arc that subtends the angle.

Hence, an angle of measure $\text{1}$ radian is subtended by the arc of length $\text{1}$ along the unit circle.

d.

To determine

Describe the measurement.

Answer to Problem 1RCC

The measure of the angle in radians is the length of the arc that subtends the angle.

Explanation of Solution

Given information:

Explain the radian measure of an angle $\theta$ .

Calculation:

Consider the following figure,

  

Hence, if the circle of the radius $1$ of is drawn with the vertex of an angle at its centre, then the measure of this angle in radians is the length of the arc that subtends the angle.

e.

To determine

Describe conversion.

Answer to Problem 1RCC

Multiply by $\frac{\pi }{180}$ .

Explanation of Solution

Given information:

Convert an angle from degree to radians.

Calculation:

The relationship between degrees and radians is given by ${180}^{\circ }=\pi rad.$

Hence, to convert degrees to radians, we multiply by $\frac{\pi }{180}$ .

f.

To determine

Describe conversion.

Answer to Problem 1RCC

Multiply by $\frac{180}{\pi }$ .

Explanation of Solution

Given information:

Convert an angle from radians to degrees.

Calculation:

The relationship between degrees and radians is given by $\frac{{180}^{\circ }}{\pi }=1rad.$

Hence, to convert degrees to radians, we multiply by $\frac{180}{\pi }$ .