NovaNET - Assignment #G2A1



Geometry Semester 2

Homework on General Angles and Radians Name: _______________________________

1. θ is an angle in standard position, with

(3, –4) on its terminal side. Find:

a. [pic] b. [pic]

c. [pic] d. [pic]

e. [pic] f. [pic]

2. Give two angles between –360o and 360o that are coterminal with each of these angles:

a. 480o b. –750o

3. Suppose [pic] and [pic]. Then the reference angle of θ is a special angle. Sketch θ in standard position, and then give the exact values of:

a. [pic] b. [pic]

c. [pic] d. [pic]

4. Convert each degree measure to radians:

a. 30o b. 150o c. 60o d. 300o

d. 180o e. 270o f. 360o g. 75o

5. Convert each radian measure to degrees:

a. [pic] b. [pic] c. [pic] d. [pic]

e. [pic] f. [pic] g. [pic] g. [pic]

6. Sketch each angle in standard position, and give the reference angle:

a. 823o b. –55o

c. 92° d. –170o

e. [pic] radians f. [pic] radians

7. Find θ to the nearest tenth of a degree (and check your answers with your calculator) if:

a. [pic]

b. [pic]

c. [pic]

d. [pic]

8. a. Use your calculator to find the value of sin 37o to 6 decimal places.

b. Now use your calculator to find the value of sin–1(0.601815) to the nearest degree.

c. Use your calculator to find the value of cos 137o to 6 decimal places.

d. Now use your calculator to find the value of cos–1(–0.731354) to the nearest degree.

e. Use your calculator to find the value of sin 137o to 6 decimal places.

f. Now use your calculator to find the value of sin–1(0.681998) to the nearest degree.

9. Use your calculator to find the values of each to the nearest degree:

a. sin–1(0.984808) b. sin–1(–0.984808)

c. cos–1(0.984808) d. cos–1(–0.984808)

e. sin–1(sin 55o) f. tan–1(tan 75o)

g. sin–1(sin 310o) h. sin–1(sin –50o)

i. cos–1(cos –50o) j. tan–1(tan 200o)

10. For what values of θ is

a. sin–1(sin θ) = θ? b. cos–1(cos θ) = θ?

c. tan–1(tan θ) = θ?

11. Give the exact values of each of the following:

a. [pic] b. [pic] c. [pic] d. [pic]

e. [pic] f. [pic] g. [pic] h. [pic]

i. [pic] j. [pic] k. [pic] l. [pic]

m. [pic] n. [pic] o. [pic] p. [pic]

12. Give two values of θ between 0 and 360 degrees where possible:

a. [pic] b. [pic]

c. [pic] d. [pic]

e. [pic] f. [pic]

g. [pic] h. [pic]

13. A circle has radius 10 cm. Find:

a. the length of an arc intercepted by a central angle measuring [pic] radians.

b. the length of an arc intercepted by a central angle measuring 135o.

c. the area of a sector intercepted by a central angle measuring [pic] radians.

d. the area of a sector intercepted by a central angle measuring 75o.

14. A bicycle wheel has a diameter of 26 inches. Someone is riding this bike.

a. When a wheel rotates one revolution, through how many radians has it rotated?

b. When each wheel has rotated one revolution, how far has the bike traveled?

c. If the bike travels a distance of 10 feet, then through how many radians has each wheel

rotated?

d. If the bike travels a distance of 10 feet, then how many rotations has each wheel made?

e. How many times has each wheel rotated when the person has gone a distance of

680.68 feet?

f. If each wheel is rotating at a rate of 100 times per minute, how fast is the person travelling (Give the answer in miles per hour.)

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( 3, –4)

θ

y

x

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