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° 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°

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

Angles of Rotation Math 4

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

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

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.

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

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

Examples…

Assignment Page 841, 9-36 all

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

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

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°

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

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

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

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°

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

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

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

Ratios:

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:

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.

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

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

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?

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

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

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.

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