Download Trig Quiz 1 Review

Algebra 2 Honors
Name________________
Date_________________
Trig Quiz 1 Review
The following problems should be done quickly and without a scientific calculator only.
1. Find the degree measure of an angle
2 Find the degree measure of an angle
in standard position determined by the
in standard position determined by the
rotation of the initial ray through one and
rotation of the initial ray through four-fifths
two-thirds of a clockwise revolution.
of a counter-clockwise revolution.
Write a formula for the measures of all angles coterminal with the given angle. Then use the formula to
find two angles, one positive and one negative, that are coterminal with the given angle.
3.
𝜃 = 370°
4.
5𝜋
7
Express in either “Decimal Degrees” or in “Degrees Minutes Seconds” to the nearest second.
5. 73° 2′
6. 119.35°
7. 16° 14′ 39′′
8. 74.89°
Find a first-quadrant angle 𝜽, for which an angle four times as large as 𝜽 will be in the given quadrant.
9. Quadrant 1
10. Quadrant 2
11. Quadrant 3
12. Quadrant 4
13. Consider an angle 𝜃 whose terminal sides passes through (−12, −13).
Find the value of all six trigonometric functions.
14. Find the six trig functions of 𝜃
√7
4
5
15. If sin 𝜃 = 6 , and cos 𝜃 < 0 find the
other five trig functions.
Find the exact value for 𝒙 𝒂𝒏𝒅 𝒚.
16.
17.
18.
60°
9
10
𝒙
45°
14
𝒙
30°
𝒙
19.
20.
32
24
𝑦
45°
21.
80
Determine the measurements for angle 𝜽 for each of the following triangles. Round to the nearest
hundredth of a degree.
22.
23.
24.
6
𝜃
13
𝜃
𝜃
11
15
12
Draw a picture for each! Round all answers to the nearest thousandth.
25. An airplane is at an elevation of 35,000 ft when it begins its approach to an airport. Its angle of
descent is 6°. What is the approximate air distance between the plane and the airport?
8
26. Find the measures of the acute angles of a right triangle whose legs are 9 cm and 16 cm long.
27. Find the measures of the angles of an isosceles triangle whose sides are 5, 10, and 10.
28. An engineer builds a 75-foot vertical cellular phone tower. Find the angle of elevation to the top of
the tower from a point on level ground 95 feet from its base.
29. Points 𝐴 and 𝐵 (on the same side of a tower) are 12 m apart. The angles of elevation of the top of a
tower are 35° and 45° respectively. Find the tower’s height.
30. A student looks out of a second-story school window and sees the top of the school flagpole at an
angle of elevation of 27°. The student is 21 ft above the ground and 75 ft from the flagpole.
Find the height of the flagpole.
31. While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation
to the peak is 6.5°. After you drive 16 miles closer to the mountain, the angle of elevation
is 14°. Approximate the height of the mountain.
Convert from Radians to Degrees, or Degrees to Radians
32. 40°
33.
7𝜋
34. 145°
6
35.
11𝜋
4
Find the sign of the expression if the terminal point determined by 𝜽 is in the given quadrant.
36. cos 𝜃 tan 𝜃; QIII
38.
tan 𝜃 sin 𝜃
cot 𝜃
37. cos 𝜃 sec 𝜃; Any Quadrant
39. 𝑡𝑎𝑛2 𝜃 sec 𝜃; QII
; QII
From the information given, find the quadrant in which 𝜽 lies.
40. sec 𝜃 > 0 and cot < 0
41. cot 𝜃 > 0 and cos > 0
42. tan 𝜃 > 0 and csc < 0
43. sin 𝜃 > 0 and cot < 0
Find the reference angle.
44. 405°
45. 840°
46.
29𝜋
6
47.
Find the exact value of the function without a calculator.
48. sin 330°
49. cot 𝜋
51. tan
5𝜋
6
52. sec 300°
54. tan
7𝜋
2
55. csc
50. cos 315°
19𝜋
6
Are the following points on the unit circle? Show your work.
21
57. (
29
20
, − 29)
16𝜋
5
58. (−
√10 3√10
, 10 )
10
53. sin
3𝜋
4
56. cos
5𝜋
3
Answers
1. −600°
4.
5𝜋
7
7.
16.24°
288°
2.
+ 2𝜋𝑛 𝑤ℎ𝑒𝑟𝑒 𝑛 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟;
11. 45° < 𝜃 < 67.5°
13. sin 𝜃 = −
13√313
,
313
3
4
cos 𝜃 = −
√7
,
4
15. sin 𝜃 = 6 , cos 𝜃 = −
17. 𝑥 =
9√2
2
22. 𝜃 = 67.38°
𝑎𝑛𝑑 −
9𝜋
7
73.03°
5.
6.
0° < 𝜃 < 22.5°
9.
10° 𝑎𝑛𝑑 −350°
119° 21′ 0′′
10. 22.5° < 𝜃 < 45°
12. 67.5° < 𝜃 < 90°
14. sin 𝜃 = , cos 𝜃 =
5
19𝜋
7
74° 53′ 24′′
8.
370 + 360𝑛 𝑤ℎ𝑒𝑟𝑒 𝑛 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟;
3.
12√313
,
313
tan 𝜃 =
√11
,
6
3√7
,
7
tan 𝜃 = −
18. 𝑥 =
28√3
3
23. 𝜃 = 56.94°
13
tan 𝜃 = 12 , csc 𝜃 = −
4
3
csc 𝜃 = , sec 𝜃 =
5√11
,
11
√313
,
13
sec 𝜃 = −
4 √7
, cot 𝜃
7
6
csc 𝜃 = 5 , sec 𝜃 = −
=
√313
, cot 𝜃
12
12
= 13
√7
3
6√11
, cot 𝜃
11
=−
√11
5
64√6
3
19. 𝑥 = 16√3
20. 𝑥 =
24. 𝜃 = 61.93°
25. 334,837.028 𝑓𝑒𝑒𝑡
16. 𝑥 = 5√3
21. 𝑥 =
320√3
3
26. 𝜃 = 29.36° 𝑎𝑛𝑑 𝜎 = 60.64°
27. 75.52° , 75.52° , 28.96°
29. 28.0276 𝑚
30. 59.21 𝑓𝑒𝑒𝑡
31. 3.357 𝑚𝑖𝑙𝑒𝑠
32.
35. 495°
36. 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒
37. 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒
38. 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒
39. 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒
40. 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 4
41. 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 1
42. 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 3
43. 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 2
44. 45°
45. 60°
46.
49. 𝑈𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑
50.
54. 𝑈𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑
55. −2
34.
29𝜋
36
√2
2
𝜋
6
51. −
56.
1
2
47.
√3
3
28. 38.29°
2𝜋
9
𝜋
5
52. 2
33. 210°
1
48. − 2
53.
57-58. 𝑌𝑒𝑠, (𝑠𝑒𝑒 𝑤𝑜𝑟𝑘)
√2
2