Lesson 5E 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 and a circumference of . How many times will the radius fit around the circumference?

A circle with radius 8 ft and Circumference 50.27 ft.

2.

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

3.

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

4.

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

Semi-circle with radius 17 cm and arc length 53.41 cm

5.

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

Semi-circle with radius 65 cm and arc length 204.2 m cm

6.

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

7.

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

8.

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

Set

9.

Circle with radius is shown.

Draw an angle of radian on circle .

Let be one side of the angle.

Circle A with radius r

10.

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

11.

Label an angle of radians on circle .

Circle A with radius r

12.

Find the ratio of as shown in the figure.

Circle A with radius r and arc MP

13.

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

Circle A with radius r with radii, AD, AC, AB, AP

14.

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

Circle A with radius r with radii, AD, AC, AB, AP

15.

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

Circle A with radius r

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

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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?

a circle

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?

a circle