Chapter 12, Problem 1CRQ

a.

To determine

To fill: The blank in the statement “The measure of the central angle subtended by an arc equal in length to the radius of the circle is called a/an _______________”.

Answer to Problem 1CRQ

The measure of the central angle subtended by an arc equal in length to the radius of the circle is called a $\underset{\_}{\text{radian}}$.

Explanation of Solution

A radian is the measure of the central angle which is subtended by an arc whose length is equal to the radius of the circle.

If s is the length of the arc subtended by a central angle $\theta$ in a circle of radius r, then $\theta =\frac{s}{r}$ radians.

Therefore, the measure of the central angle subtended by an arc equal in length to the radius of the circle is called a $\underset{\_}{\text{radian}}$.

b.

To determine

To fill: The blank in the statement “The angle subtended by one complete revolution is _____ radians or _____ degrees”.

Answer to Problem 1CRQ

The angle subtended by one complete revolution is $\underset{\_}{\text{2}\pi }$ radians or $\underset{\_}{360}$ degrees.

Explanation of Solution

An initial ray in standard position through one complete revolution, obtain an angle of 360 degrees or $\text{2}\pi$ radians.

That is, an angle whose measure is 360 degrees or $\text{2}\pi$ radians is called a complete angle.

Therefore, the angle subtended by one complete revolution is $\underset{\_}{\text{2}\pi }$ radians or $\underset{\_}{360}$ degrees.