Quiz 6.1-6.3 REVIEW
Name:_____________________________
Hour:______
Pre-Calculus
Convert from radians to degrees or from degrees to radians.
1. 72º
2. -120º
3.
7𝜋
6
4. −
11𝜋
3
Find two positive angles and two negative angles that are coterminal with the given angle.
𝜋
5. 50º
6. − 4
7. Find an angle between 0º and 360º
that is coterminal with -800º.
8. Find an angle between 0 and 2π
17𝜋
that is coterminal with − 4 .
9. Find the length of arc s in the figure.
10. An arc of length 60m subtends a central
angle θ in a circle of radius 20m. Find θ in
radians.
120º
4
s
11. A sector of a circle has a central angle
of 62º. Find the area of the sector if the
radius of the circle is 3 mi.
12. The area of a sector of a circle is 16 m2. If
the central angle is 2 radians, find the
radius of the circle.
13. The wheels of a car have a radius of 11 inches and rotate at 600 rpm. Find the speed of the car in
mi/hr.
14. A truck has 48-inch diameter wheels that rotate at 520 rpm.
a) Find the angular speed of the wheels in rad/min.
b) Find the linear speed of the wheels in mi/hr.
15. Find the exact values of the six trig functions for angle θ in the triangle below.
θ
sin θ =
csc θ =
3
cos θ =
sec θ =
tan θ =
cot θ =
2
Find the value of x. Use exact values when possible.
16.
17.
30º
x
x
20
32
68º
62º
18. Sketch a triangle that has an acute angle θ. If cot θ = 1, find the values of the other five trig
functions for angle θ.
sin θ =
cos θ =
csc θ =
sec θ =
tan θ =
19. Evaluate the expression without using a calculator: sin 30° ∙ csc 30°
Solve the right triangle.
B
20.
21.
48º
30
C
B
106
A
𝜋
5
A
C
A=
B=
C=
A=
B=
C=
a=
b=
c=
a=
b=
c=
22. A child is on a beach flying a kite. He holds the end of the kite string at ground level and
estimates the angle of elevation of the kite to be 50º. If the string is 450 feet long, then how high is
the kite above ground?
23. When the moon is exactly half full, the earth, moon, and sun form a right angle. At that time, the
angle formed by the sun, earth, and moon is measured to be 89.85º. If the distance from the
earth to the moon is 240,000 miles, estimate the distance from the earth to the sun.
24. From the top of a 150-ft. lighthouse, the angle of depression to a ship in the ocean is 35º. How far
is the ship from the base of the lighthouse?
Find the reference angle for the given angle. (Write your answers in the form given!!)
25. 225º
28.
26. 810º
4𝜋
3
29.
27. -105º
33𝜋
4
30. −
5𝜋
6
Find the EXACT VALUE of the trig function. SHOW YOUR WORK!!!
31. sin 225º
5𝜋
34. tan ( 6 )
32. cos (-60º)
33. tan (750º)
5𝜋
35. csc ( 4 )
36. sec (−
2𝜋
)
3
Find the quadrant in which θ lies given the following information.
37. tan θ < 0 and sin θ < 0
38. csc θ > 0 and cos θ < 0
Find the values of the remaining five trig functions of θ given the following information.
1
39. csc θ = 2, θ is in Quadrant 1
40. cot θ = 4, sin θ < 0
sin θ =
cos θ =
tan θ =
sin θ =
cos θ =
sec θ =
cot θ =
csc θ =
sec θ =
tan θ =
41. A triangle has an area of 16 in2, and two sides of the triangle have lengths 5 in. and 7 in. Find the
angle included by these two sides.
42. Find the area of the shaded region in the figure.
150º
4
Answers:
1.
2𝜋
2𝜋
2. −
5
10. 3 rad.
15. sin 𝜃=
11.
2√13
13
18. sin 𝜃 =
20
mi2
cos 𝜃 =
21. A = , B =
𝜋
3𝜋
2
10
27. 75˚
𝜋
1
31𝜋
3
41. 66.1˚
13
√2
,
2
5. 410˚, 770˚, -310˚, -670˚
13. 39.3 mi/hr
2
√13
,
2
, tan 𝜃 = , csc 𝜃 =
3
5
29.
𝜋
30.
4
√3
,
2
√13
,
3
tan 𝜃 = 1, csc 𝜃 = √2, sec 𝜃 = √2
𝜋
𝜋
6
tan 𝜃 =
42. 16.94 units2
31. −
√3
,
3
√2
2
sec 𝜃 =
32.
2√3
3
1
2
cot 𝜃 =
19. 1
22. 344.72 ft.
33.
, cot 𝜃 = √3
6.
7𝜋 15𝜋
4
,
4
,−
9𝜋
4
,−
17𝜋
4
14a. 3267.3 rad/min
sec 𝜃 =
, C = , a = 180.3, b = 145.9, c = 106
39. sin 𝜃 = , cos 𝜃 =
2
4. -660˚
12. 4 m.
3√13
, cos 𝜃 =
√2
,
2
28.
3. 210˚
3
√3
3
34.
3
8.
7𝜋
9.
4
16𝜋
3
14b. 74.3 mi/hr
16. x = 16
2
7. 280˚
17. x = 24.43
20. A = 90˚, B = 48˚, C = 42˚, a = 44.8, b = 33.3, c = 30
23. 91,673,351.94 miles
−√3
35. −√2
3
40. sin 𝜃 =
−4√17
17
, cos 𝜃 =
36. -2
−√17
17
24. 214.2 ft. 25. 45˚
37. Q4
26. 90˚
38. Q2
, tan 𝜃 = 4, csc 𝜃 =
−√17
4
, sec𝜃 = −√17