merrill pg. 759
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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° - PowerPoint PPT PresentationTRANSCRIPT
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