1. Write the expression in simplest form.
(180º) 5 6
ANSWER
150º 2.
115º
180º 36
ANSWER 23

2. Write the expression in simplest form.11 12 3.
(180º)
ANSWER
165º 4.
135º
180º
ANSWER 3 4

3. Write the expression in simplest form.
5. A compact disc has radius 6 centimeters. Find its circumference and area to the nearest tenth.
ANSWER
C cm; A cm2

4. EXAMPLE 1
Draw angles in standard position
Draw an angle with the given measure in standard position.
a. 240º
SOLUTION
a. Because 240º is 60º more than 180º, the terminal side is 60º counterclockwise past the negative x-axis.

5. EXAMPLE 1
Draw angles in standard position
Draw an angle with the given measure in standard position.
b º
SOLUTION
b. Because 500º is 140º more than 360º, the terminal side makes one whole revolution counterclockwise plus 140º more.

6. EXAMPLE 1
Draw angles in standard position
Draw an angle with the given measure in standard position.
c. –50º
SOLUTION
c. Because –50º is negative, the terminal side is 50º clockwise from the positive x-axis.

7. EXAMPLE 2
Find coterminal angles
Find one positive angle and one negative angle that are coterminal with (a) –45º and (b) 395º.
SOLUTION
There are many such angles, depending on what multiple of 360º is added or subtracted.
a. –45º + 360º
= 315º
–45º – 360º
= – 405º

8. EXAMPLE 2
Find coterminal angles
= –325º
b. 395º – 360º
= 35º
395º – 2(360º)

9. GUIDED PRACTICE
for Examples 1 and 2
Draw an angle with the given measure in standard position. Then find one positive coterminal angle and one negative coterminal angle. 1.
65°
65º + 360º
= 425º
65º – 360º
= –295º 2.
230°
230º + 360º
= 590º
230º – 360º
= –130º

10. GUIDED PRACTICE
for Examples 1 and 2 3.
300°
300º + 360º
= 660º
300º – 360º
= –60º 4.
740°
740º – 2(360º)
= 20º
740º – 3(360º)
= –340º

11. ( ) ( ) EXAMPLE 3 Convert between degrees and radians
Convert (a) 125º to radians and (b) – radians to degrees. π 12 (
π radians
180º )
= 125º
a. 125º
25π 36 =
radians b. π 12 –
π radians
180º π 12 – =
radians ( ) =
–15º

12. ( ) GUIDED PRACTICE for Example 3
Convert the degree measure to radians or the radian measure to degrees. 5.
135° (
π radians
180º )
= 135º
135º 3π 4 =
radians

13. ( ) ( ) GUIDED PRACTICE for Example 3 6. –50° π radians –50° = –50°
180º )
= –50°
–50°
– 5π 18 =
radians 7. 5π 4 5π 4
π radians
180º 5π 4 =
radians ( )
= 225º

14. ( ) GUIDED PRACTICE for Example 3 π 8. 10 π π 180º radians = 10 10
= 18º

15. EXAMPLE 4
Solve a multi-step problem
Softball
A softball field forms a sector with the dimensions shown. Find the length of the outfield fence and the area of the field.

16. ( ) EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1
Convert the measure of the central angle to radians.
90º = 90º (
π radians
180º ) = π 2
radians

17. ( ) ( ) EXAMPLE 4 Solve a multi-step problem STEP 2
Find the arc length and the area of the sector. π
Arc length: s = r = = 90π ≈ 283 feet θ 2 ( )
Area: A = r2θ = (180) = π ≈ 25,400 ft2 π 2 ( ) 1
The length of the outfield fence is about 283 feet. The area of the field is about 25,400 square feet.
ANSWER

18. ( ) GUIDED PRACTICE for Example 4 9.
What If? In Example 4, estimate the length of the outfield fence and the area of the field if the outfield fence is 220 feet from home plate.
SOLUTION
STEP 1
Convert the measure of the central angle to radians.
90º = 90º (
π radians
180º )
radians = π 2

19. ( ) ( ) GUIDED PRACTICE for Example 4 STEP 2
Find the arc length and the area of the sector. π
Arc length: s = r = = 110π ≈ 346 feet θ 2 ( )
Arc length: A = r2θ = (220) = π ≈ 38,013 ft2 π 2 ( ) 1
The length of the outfield fence is about 346 feet. The area of the field is about 38,013 square feet.
ANSWER

20. Daily Homework Quiz
Find one positive angle and one negative angle that are conterminal with 475°. 1.
115°; –245°
ANSWER 2.
Convert 315° to radians and radians to degrees.
17π 6
ANSWER
radians; 510° 7π 4

21. Daily Homework Quiz 3.
You are planting a vegetable garden on a plot of land that is a sector of a circle. You want fencing along only the curved edge of the garden. Use the figure to find the length of fencing you will need and the area that will be available for planting.
ANSWER
about 19.6 ft; about 147 ft2