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Write the expression in simplest form.

1. (180º). 150º. ANSWER. 5. 6. 115º. 2. 180º. 23. ANSWER. 36. Write the expression in simplest form. 11. 12. (180º). 3. 165º. ANSWER. 135º. 180º. 3. 4. 4. ANSWER. Write the expression in simplest form. ANSWER. C 37.7 cm ; A 131.1 cm 2.

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Write the expression in simplest form.

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

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

  3. ANSWER C37.7cm; A131.1cm2 Write the expression in simplest form. 5. A compact disc has radius 6 centimeters. Find its circumferenceand area to the nearest tenth.

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

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

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

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

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

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

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

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

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

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

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

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

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

  17. π ) ( Arc length: s=r= 180 = 90π ≈ 283 feet θ 2 π 1 1 ) ( Area: A=r2θ= (180)2 = 8100π ≈ 25,400 ft2 2 2 2 ANSWER The length of the outfield fence is about 283feet. The area of the field is about 25,400square feet. EXAMPLE 4 Solve a multi-step problem STEP 2 Find the arc length and the area of the sector.

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

  19. ) ( Arc length: s=r= 220 = 110π ≈ 346 feet θ 2 π 1 1 ) ( Arc length: A=r2θ= (220)2 = 12100π ≈ 38,013 ft2 2 2 2 ANSWER The length of the outfield fence is about 346feet. The area of the field is about 38,013square feet. for Example 4 GUIDED PRACTICE STEP 2 Find the arc length and the area of the sector. π

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

  21. 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 147ft2 Daily Homework Quiz

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