Lesson 8 Rays and Radians Solidify Understanding

Ready

The diagrams are provided to help you visualize your response to the problems. Answers should be rounded to two decimal places.

1.

A circle has a radius of $8 feet$ and a circumference of $50.27 feet$ . How many times will the radius fit around the circumference?

2.

A circle has a radius of $15 inches$ and a circumference of $94.25 inches$ How many times will the radius fit around the circumference?

3.

If an angle measures $2 π radians$ , what is the measure of the angle in degrees?

4.

A semicircle has a radius of $17 centimeters$ . The arc of the semicircle measures $53.41 centimeters$ . How many times will the radius fit around the arc of the semicircle?

5.

A semicircle has a radius of $65 meters$ . The arc of the semicircle measures $204.2 meters$ . How many times will the radius fit around the arc of the semicircle?

6.

If an angle measures $π radians$ , what is the measure of the angle in degrees?

7.

If there are $360 °$ in a full circle, how many radians are there in a full circle?

8.

If an angle measures $1 radian$ , what is the measure of the angle in degrees?

Set

9.

Circle $A$ with radius $r$ is shown.

Draw an angle of $1$ radian on circle $A$ .

Let $\overset{―}{A P}$ be one side of the angle.

10.

If you laid the radius end to end around the circumference of $⨀ A$ , how many radii would it take to fit exactly?

11.

Label an angle of $π$ radians on circle $A$ .

12.

Find the ratio of $\frac{measure of arc MP}{r}$ as shown in the figure.

13.

One half of circle $A$ has been divided into $4$ equal parts. Label points $B$ , $C$ , and $D$ with the radian measures of angles $B A P$ , $C A P$ , and $D A P$ . Then write the corresponding degree measure for each angle.

14.

One half of circle $A$ has been divided into $3$ equal parts. Label points $E$ and $F$ with the radian measures of angles $E A P$ and $F A P$ . Then write the corresponding degree measure for each angle.

15.

What are the radian and degree measures of the angle of rotation from $0$ to $P$ in a counterclockwise direction?

Find the equivalent radian or degree measure of each angle based on what is given:

16.

$100 ° =$ $radians$

17.

$30 ° =$ $radians$

18.

$225 ° =$ $radians$

19.

$\frac{π}{5} radians =$ °

20.

$\frac{5 π}{6} radians =$ °

Go

21.

Locate the center of the circle.
Draw a central angle and an inscribed angle that cuts the same arc as the central angle. What is the relationship between the measure of a central angle and its corresponding inscribed angle?

22.

Locate the center of the circle.
Draw a central angle and a circumscribed angle that cuts the same arc as the central angle. What is the relationship between the measure of a central angle and its corresponding circumscribed angle?