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Merrill pg. 759

Merrill pg. 759. Find the measures of all angles and sides Their sum is 90° They are equal a = 9.6 b = 3.2 c = 13.3 b = 7.3 c = 13.5 c = 11.6. Continued…. b = 6, A = 53°, B = 37° b = 5, A = 67°, B = 23° c = 7.3, A = 16°, B = 74° a = 10.8, A = 31°, B = 59°

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Merrill pg. 759

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  1. Merrill pg. 759 • Find the measures of all angles and sides • Their sum is 90° • They are equal • a = 9.6 • b = 3.2 • c = 13.3 • b = 7.3 • c = 13.5 • c = 11.6

  2. Continued… • b = 6, A = 53°, B = 37° • b = 5, A = 67°, B = 23° • c = 7.3, A = 16°, B = 74° • a = 10.8, A = 31°, B = 59° • c = 23.7, A = 28°, B = 62° • a = 11.5, A = 63°, B = 27° • B = 27°, c = 10.9, b = 4.9 • a = 3.9, b = 13.5, B = 74°

  3. Continued… • B = 53°, c = 13.9, a = 8.4 • A = 48°, c = 12.1, b = 8.2 • A = 26°, a = 8.4, b = 17.3 • A = 7°, a = 0.7, c = 5.7 • A = 57°, c = 39.4, b = 21.4 • A = 77°, a = 5.9, b = 1.4 • B = 13°, a = 181.9, c = 186.7 • A = 41°, b = 10.4, c = 13.7 • B = 68°, a = 9.1, c = 23.8 • A = 46°, c = 61.9, b = 43.6

  4. Angles of Rotation Math 4

  5. Essential Question: • How do I find coterminal and reference angles for angles of rotation?

  6. Vocabulary • Angle of Rotation: The position of a rotated ray relative to its starting position • Initial Side: The starting position of a ray (positive side of the x-axis) • Terminal Side: The final position of a ray of an angle • Standard Position: When the initial side lies along the positive x-axis and its endpoint is at the origin

  7. Vocabulary continued… • Positive Measure: The direction of rotation is counter-clockwise • Negative Measure: The direction of rotation is clockwise • Degree: The unit used for angle measurement • Coterminal Angles: Two angles that have the same terminal side • Reference Angles: Always positive, 90° or less, and if the angle of rotation is an acute angle, then the reference angle will be the angle itself.

  8. To find coterminal angles… • Add 360° to the given angle of rotation • Subtract 360° from the given angle of rotation • Continue adding and subtracting 360° until all angles that lie between -360° and +360° are found

  9. To find reference angles… • Draw the given angle of rotation • Find the angle measure formed by the nearest x-axis and the terminal side of the angle of rotation

  10. Examples…

  11. Assignment • Page 841, 9-36 all

  12. Do Now: For each angle find all coterminal angles and the corresponding reference angle: • 37° • -184° • 715° • -417°

  13. Do Now Answers: • -323°; 37° • 176°; 4° • 355°, -5°; 5° • -57°, 303°; 57°

  14. Pg. 841, 9-36 all 9 – 12 sketched 13. -325°; 35° 14. -337°; 23° 15. -248°; 68° 16. -200°; 20° 17. 252°, -108°; 72° 18. 118°, -242°; 62° 19. 225°; 45° 20. 45°; 45° 21. -270°; 90° 22. 180°; 0° 23. -90°, 270°; 90° 24. -125°, 235°; 55° 25. 180°, -180°; 0° 26. -90°; 90° 27. -135°; 45° 28. -165°; 15° 29. 50°, -310°; 50° 30. 200°, -160°; 20°

  15. Continued… 31. 240°; 60° 32. 80°; 80° 33. 185°; 5° 34. 65°; 65° 35. -35°, 325°; 35° 36. -180°, 180°; 0°

  16. Assignment • Page 983 - 13.2, 1-12 • Workbook page 83 - 13.2, 1-18

  17. Do now: Find the coterminal angle(s) and the corresponding reference angle for: 1. -200° 2. 53° 3. 852°

  18. Worksheet – 13.2, 1-18 • -313°; 47° • 237°; 57° • -142°; 38° • 152°, -208°; 28° • 138°; 42° • -53°; 53° • 42°, -318°; 42° • 175°; 5° • 285°, -75°; 75° 10. 75° 11. 33° 12. 5° 13. 36° 14. 40° 15. 72° 16. 2° 17. 80° 18. 60°

  19. Pg. 983 – 13.2, 1-12 • -246° • -338° • 307° • 88° • 152°, -208° • -135°, 225° • 63° • 78° • 56° • 28° 11. 65° 12. 49°

  20. 13.2 continued… Essential Question: How do I find the values of the 6 trig functions of angles in standard position?

  21. Steps… If a point on the terminal side is given: • Substitute the values for X and Y then solve for R using the Pythagorean theorem • Use X, Y, R, and the 6 trig functions to write the ratios • Simplify the ratios by rationalizing the denominator if necessary

  22. Ratios:

  23. Example 1 • Find the exact values of the six trig functions of θ given the point (-2, -3) on the terminal side of angle θ in standard position:

  24. Example 2 • Find the exact values of the six trig functions of θ given the point (-3, 1) on the terminal side of angle θ in standard position.

  25. Assignment: • Pg. 841, 37-47 (omit 45)

  26. Do Now: • Draw a coordinate plane and label the quadrants. • Convert these decimals into fractions: a) .25 b) -1.2 c) -1.75 d) .4

  27. The Last Part of 13.2… • Essential Question: • How do I find any trig function of θ when given a quadrant and one trig function of the terminal side of θ?

  28. Steps… • Convert any decimals to reduced fractions • Use Pythagorean Theorem • PAY ATTENTION TO SIGNS!!!

  29. Example 1 • The terminal side of θ in standard position is in Quadrant II, and cosθ = . Find the exact values of the six trig functions of θ.

  30. Example 2 • The terminal side of θ in standard position is in Quadrant III, and sin θ = . Find the exact values of the six trig functions of θ.

  31. Assignment • Pg. 841, 37-55 all (omit 45) • Please note that you are only asked to find ONE function in each problem from #’s 48-55… • Quiz over 13.2 WEDNESDAY

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