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 °; 35° °; 23° °; 68° °; 20° °, -108°; 72° °, -242°; 62° °; 45° °; 45°
°; 90° °; 0° °, 270°; 90° °, 235°; 55° °, -180°; 0° °; 90° °; 45° °; 15° °, -310°; 50° °, -160°; 20°

15. Continued…
°; 60° °; 80° °; 5° °; 65° °, 325°; 35° °, 180°; 0°

17. Assignment
Page , 1-12
Workbook page , 1-18

18. Do now:
Find the coterminal angle(s) and the corresponding reference angle for: ° 2. 53° °

19. 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° ° 12. 5° ° ° ° 16. 2° ° °

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

21. 13.2 continued… Essential Question:
How do I find the values of the 6 trig functions of angles in standard position?

22. 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

23. Ratios:

24. 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:

25. 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.

26. Assignment:
Pg. 841, (omit 45)

27. Do Now: Draw a coordinate plane and label the quadrants.
Convert these decimals into fractions:
a) .25 b) c) d) .4

28. 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?

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

30. 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.

32. 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.

34. 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