Merrill pg. 759

1. Find the measures of all angles and sides2. Their sum is 90°3. They are equal4. a = 9.65. b = 3.26. c = 13.37. b = 7.38. c = 13.59. c = 11.6

Continued…

10. b = 6, A = 53°, B = 37°11. b = 5, A = 67°, B = 23°12. c = 7.3, A = 16°, B = 74°13. a = 10.8, A = 31°, B = 59°14. c = 23.7, A = 28°, B = 62°15. a = 11.5, A = 63°, B = 27°16. B = 27°, c = 10.9, b = 4.917. a = 3.9, b = 13.5, B = 74°

Continued…

18. B = 53°, c = 13.9, a = 8.419. A = 48°, c = 12.1, b = 8.220. A = 26°, a = 8.4, b = 17.321. A = 7°, a = 0.7, c = 5.722. A = 57°, c = 39.4, b = 21.423. A = 77°, a = 5.9, b = 1.424. B = 13°, a = 181.9, c = 186.725. A = 41°, b = 10.4, c = 13.726. B = 68°, a = 9.1, c = 23.827. 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:

1. 37°2. -184°3. 715°4. -417°

Do Now Answers:

1. -323°; 37°2. 176°; 4°3. 355°, -5°; 5°4. -57°, 303°; 57°

Pg. 841, 9-36 all

9 – 12 sketched13. -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

1. -313°; 47°2. 237°; 57°3. -142°; 38°4. 152°, -208°; 28°5. 138°; 42°6. -53°; 53°7. 42°, -318°; 42°8. 175°; 5°9. 285°, -75°; 75°

10. 75°11. 33°12. 5°13. 36°14. 40°15. 72°16. 2°17. 80°18. 60°

1. -246°2. -338°3. 307°4. 88°5. 152°, -208°6. -135°, 225°7. 63°8. 78°9. 56°10. 28°

Pg. 983 – 13.2, 1-12

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:

1. Draw a coordinate plane and label the quadrants.

2. 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.

35

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.

45

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