Download Advanced Math Review 5.1-5.2 Quiz Name: February 2016 Find the

Advanced Math
Review 5.1-5.2 Quiz
Name:
February 2016
Find the measure of the complement and supplement (if possible) for each angle.
𝜋
6
2𝜋
3
1. 112°
2. 25°
3.
1. Comp.:_______
2. Comp.:_______
3. Comp.:_______
4. Comp.:_______
1. Supp.:_______
2. Supp.:_______
3. Supp.:_______
4. Supp.:_______
4.
Determine the measure of the positive angle with measure less than 𝟑𝟔𝟎° that is coterminal with the given angle.
Then classify the angle by quadrant. Assume the angles are in standard position.
5. 790°
6. 1123°
7. −900°
8. −1052°
5. Coterminal:_______
6. Coterminal:_______
7. Coterminal:_______
8. Coterminal:_______
5. Quadrant:_______
6. Quadrant:_______
7. Quadrant:_______
8. Quadrant:_______
~What is the formula to convert from degrees to radians?
Convert the degree measure to exact radian measure.
9. 45°
10. −120°
11. −210°
12. 315°
9. Radians:_______
10. Radians:_______
11. Radians:_______
12. Radians:_______
~What is the formula to convert from radians to degrees?
Convert the radian measure to exact degree measure.
13.
2𝜋
5
13. Degrees:_______
14. –
3𝜋
4
14. Degrees:_______
15. –
2𝜋
9
15. Degrees:_______
16.
7𝜋
12
16. Degrees:_______
Use your calculator to convert the degree measure to radian measure. Round your answers to the nearest hundredth.
17. 72°
18. −103°
17. Radians:_______
18. Radians:_______
Use your calculator to convert the radian measure to degree measure. Round your answers to the nearest hundredth.
19.
2𝜋
7
20. 10.25
19. Degrees:_______
20. Degrees:_______
~What is the formula to find arc length?
Find the measure in radians and degrees of the central angle of a circle subtended by the given arc. Round
approximate answers to the nearest hundredth.
21. 𝑟 = 4 inches,
𝑠 = 15 inches
21. 𝜃 = _________
22. 𝑟 = 3.2 meters,
𝑠 = 5.8 meters
22. 𝜃 = _________
Find the length of the arc that subtends a central angle with the given measure in a circle with the given radius.
Round answers to the nearest hundredth.
23. 𝑟 = 6 yards,
𝜃=
𝜋
5
23. 𝑠 = _________
24. 𝑟 = 7.2 feet,
𝜃=
4𝜋
9
24. 𝑠 = _________
~What is the formula to find the area of a sector?
Find the area, to the nearest square unit, of the sector of a circle with the given radius and central angle.
25. 𝑟 = 7 mm,
𝜃=
25. 𝐴 = _________
𝜋
3
radians
26. 𝑟 = 30 cm,
𝜃 = 0.75 radians
26. 𝐴 = _________
27. Find the values of the six trig functions of 𝜃 for the right triangle given. Reduce all ratios when appropriate.
𝐬𝐢𝐧 𝜽 =
𝐜𝐬𝐜 𝜽 =
𝐜𝐨𝐬 𝜽 =
𝐬𝐞𝐜 𝜽 =
𝐭𝐚𝐧 𝜽 =
𝐜𝐨𝐭 𝜽 =
𝜃
10
6
28. Find the values of the six trig functions of 𝜃 for the right triangle given. Reduce all ratios when appropriate.
𝐬𝐢𝐧 𝜽 =
𝐜𝐬𝐜 𝜽 =
𝐜𝐨𝐬 𝜽 =
𝐬𝐞𝐜 𝜽 =
𝐭𝐚𝐧 𝜽 =
𝐜𝐨𝐭 𝜽 =
𝜃
3
5
29. Let 𝜃 be an acute angle of a right triangle for which sin 𝜃 =
7
.
25
Find the other five trig functions. Draw a
triangle first and label all the sides!
𝐬𝐢𝐧 𝜽 =
𝐜𝐬𝐜 𝜽 =
𝐜𝐨𝐬 𝜽 =
𝐬𝐞𝐜 𝜽 =
𝐭𝐚𝐧 𝜽 =
𝐜𝐨𝐭 𝜽 =
2
30. Let 𝜃 be an acute angle of a right triangle for which tan 𝜃 = 7. Find the other five trig functions. Draw a
triangle first and label all the sides!
𝐬𝐢𝐧 𝜽 =
𝐜𝐬𝐜 𝜽 =
𝐜𝐨𝐬 𝜽 =
𝐬𝐞𝐜 𝜽 =
𝐭𝐚𝐧 𝜽 =
𝐜𝐨𝐭 𝜽 =
~Label the sides of this 𝟑𝟎° − 𝟔𝟎° − 𝟗𝟎° triangle
60°
30°
~Label the sides of this 𝟒𝟓° − 𝟒𝟓° − 𝟗𝟎° triangle.
45°
45°
𝐬𝐢𝐧 𝟑𝟎° =
𝐜𝐬𝐜 𝟑𝟎° =
𝐬𝐢𝐧 𝟔𝟎° =
𝐜𝐬𝐜 𝟔𝟎° =
𝐜𝐨𝐬 𝟑𝟎° =
𝐬𝐞𝐜 𝟑𝟎° =
𝐜𝐨𝐬 𝟔𝟎° =
𝐬𝐞𝐜 𝟔𝟎° =
𝐭𝐚𝐧 𝟑𝟎° =
𝐜𝐨𝐭 𝟑𝟎° =
𝐭𝐚𝐧 𝟔𝟎° =
𝐜𝐨𝐭 𝟔𝟎° =
𝐬𝐢𝐧 𝟒𝟓° =
𝐜𝐬𝐜 𝟒𝟓° =
𝐜𝐨𝐬 𝟒𝟓° =
𝐬𝐞𝐜 𝟒𝟓° =
𝐭𝐚𝐧 𝟒𝟓° =
𝐜𝐨𝐭 𝟒𝟓° =
31. Find sin 60° + cos 30°
31.)_______________________
32. Find csc 30° + sin 60°
32.)_______________________
𝜋
𝜋
33. Find sin 6 − cos 3
34. Find sin
𝜋
6
cos
33.)_______________________
𝜋
3
34.)_______________________
35. Use your calculator to find the value of the trigonometric function to four decimal places (nearest ten
thousandth). Don’t forget to check the mode of your calculator before doing these!!
a.
cos
𝜋
8
b.
sec
𝜋
10
35a.)______________________
35b.)______________________
c.
cot 216°
d.
csc 114.75°
35c.)______________________
35d.)______________________
Round answers to the nearest tenth.
36. A rocket is fired in the air at an angle of elevation of 62°. When the rocket is a ground distance of 1.5 miles
away, what is its height?
36.)________________
37. From a point 230 meters from the base of an apple tree, the angle of elevation to the top of the tree is 59.6°.
Find the height of the tree to the nearest meter.
37.)________________
38. A 50-foot ladder is leaning against a building. The angle of elevation of the ladder to the top of the building is
14.8°. How far away is the ladder from the base of the building?
38.)________________
39. A 65-foot ladder is leaning against a house. The angle the ladder makes with the building is 52.3°.
How far away is the base of the ladder from the house?
39.)________________
40. An airplane is flying at an altitude of 15,000 feet. The pilot spots the far end of the runway at an angle of
depression of 38°. What is the ground distance to the far end of the runway?
40.)________________
41. Two children are playing up in a tree house that is 25 feet off the ground. There is a special slide they can
use to exit the tree house. They see the slide at an angle of depression of 20°. How long is the slide?
41.)________________
Answers:
𝜋
3
5𝜋
6
𝜋
3
1. Comp.: None; Supp: 68°
2. Comp: 65°; Supp: 155°
3. Comp:
5. Cot. : 70° ; Quad.: 1
6. Cot. : 43° ; Quad.: 1
7. Cot.: 180° ; Quad.: None, on the axis (quadrantal)
8. Cot. : 28° ; Quad.: 1
9.
14. −135°
16. 105°
15. −40°
21. 3.75 radians
𝜋
4
10. −
2𝜋
3
17. 1.26
22. 1.8125 radians
11. −
; Supp:
7𝜋
6
18. −1.80
26. 337.5 cm2
27. cos 𝜃 =
tan 𝜃 =
5√34
34
3√34
cos 𝜃 = 34
5
tan 𝜃 = 3
√34
5
√34
sec 𝜃 = 3
3
cot 𝜃 = 5
29. cos 𝜃 =
2√53
53
7√53
cos 𝜃 =
53
2
tan 𝜃 = 7
√53
2
√53
sec 𝜃 =
7
7
cot 𝜃 = 2
31. √3
sin 𝜃 =
28.
sin 𝜃 =
30.
34.
1
4
36. 2.82 mi
41. 73.10 ft
csc 𝜃 =
7𝜋
4
13. 72°
19. 51.43°
23. 3.77 yards
sin 𝜃 =
25. 25.66 mm2
12.
4. Comp: None; Supp:
sin 𝜃 =
tan 𝜃 =
4
5
3
5
4
3
7
25
24
25
7
24
20. 587.28°
24. 10.05 feet
csc 𝜃 =
sec 𝜃 =
cot 𝜃 =
5
4
5
3
3
4
csc 𝜃 =
sec 𝜃 =
cot 𝜃 =
25
7
25
24
24
7
csc 𝜃 =
32.
4 + √3
2
33. 0
35a. 0.9239
35b. 1.0515
35c. 1.3764
35d. 1.1011
37. 392.03 mi
38. 48.34 ft
39. 51.43 ft
40. 19,199.12 ft