Precalculus
Final Exam Review Sheet
1)
Convert the angle 75 D15'20" to degrees.
2)
Convert 167.79º to degrees, minutes, seconds.
3)
If s denotes the length of the arc of a circle of radius r subtended by a central
angle θ, find the missing quantity.
R = 9.87 in, θ=20º, s = ?
4)
5)
If s denotes the length of the arc of a circle of radius r subtended by a central
angle θ, find the missing quantity.
R = 8 feet , s = 20 feet ,ϑ = ?
Convert 48º to radians.
6)
Convert -450º to radians.
7)
Convert
8)
Convert −
9)
If A denotes the area of a section of a circle of radius r formed by the central
angle θ, find the missing quantity in the information given below.
R = ?, θ = 5 radians, A = 30 square meters
10)
11)
3π
to degrees.
10
23π
to degrees.
8
⎛
33 4 ⎞
,− ⎟⎟ is the point on the unit circle that corresponds to t.
Point P ⎜⎜ −
7
7⎠
⎝
Find the exact value of cot t .
⎛ 39 5 ⎞
, ⎟⎟ is the point on the unit circle that corresponds to t. Find
Point P ⎜⎜
8
8⎠
⎝
the exact value of sec t .
12)
The point (6, 8) lies on the terminal side of angle θ. Find the exact value of
csc θ.
13)
The point (-8, -5) lies on the terminal side of angle θ. Find the exact value of
tan θ.
Precalculus
Final Exam Review Sheet
3π
?
2
14)
What is the value of tan
15)
What is the value of cos 45 D ?
16)
What is the value of cot 60 D ?
17)
What is the value of csc 30 D − cos 30 D ?
18)
What is the value of sec
19)
What is the value of sin 135 D + sin 270 D ?
20)
What is the range of the cosine function?
21)
In what quadrant does θ lie if cot θ < 0 and cos θ > 0?
22)
If cos ϑ =
23)
3
If cot ϑ = − and cos ϑ < 0, find cscϑ .
8
24)
What is the amplitude of y = −3 cos 4 x ?
25)
What is the period of y =
26)
⎛1 ⎞
Determine the amplitude and period of y = −8 sin ⎜ x ⎟
⎝4 ⎠
27)
1
Graph y = 3 cos( x) .
2
28)
Write the equation of a sine function with amplitude = 3 and period = to 4.
29)
What is the equation for the sine function with amplitude 4, period 3π , and
21π
?
4
4
and tan ϑ < 0, find sin ϑ .
9
phase shift
π
3
?
1
⎛ 6π
cos⎜
2
⎝ 7
⎞
x⎟ ?
⎠
Precalculus
Final Exam Review Sheet
1
1
−
.
2
cos ϑ cot 2 ϑ
30)
Establish the identity for
31)
Establish the identity for sin 2 ϑ + tan 2 ϑ + cos 2 ϑ .
32)
Establish the identity for tan ϑ (cot ϑ − cos ϑ ) .
33)
Establish the identity for
34)
Use sum and difference formulas to find the value of sin195D .
35)
Use sum and difference formulas to find the value of
sin 20 D cos 40 D + cos 20 D sin 40 D .
36)
If
csc ϑ cot ϑ
.
sec ϑ
40)
20 3π
12 π
,
< α < 2π and tan β = − , < β < π find cos(α + β ).
29 2
5 2
3 π
1 π
If sin α = , < α < π and cos β = − , < β < π find sin(α − β ).
4 2
3 2
7
π
If cos ϑ =
, 0 <ϑ <
find sin( 2ϑ ).
25
2
5 21
If sec ϑ = −
, csc ϑ > 0 find cos(2ϑ ).
21
Solve the equation 2 cos ϑ = 3 .
41)
Solve the equation sin ϑ + 1 = 0 .
42)
Solve the equation 2 sin 2 ϑ = sin ϑ .
43)
Solve the triangle using the information given. Round to two decimal places
if necessary.
A = 10 D , B = 80 D , a = 1
44)
Given a triangle with b = 4, c = 5, and A = 62 D , what is the length of a?
45)
lim
( −3 x 2 + 7 x )
x → −1
sin α = −
37)
38)
39)
Precalculus
Final Exam Review Sheet
46)
lim
x+2
3x − 4
x→0
47)
lim
⎛ h 2 + 4h + 3 ⎞
⎟⎟
⎜⎜
⎝ h+3 ⎠
h → −3
48)
lim
x → 16
⎛ x − 16 ⎞
⎜
⎟
⎝ x −4⎠
1
49)
lim
(4 x 3 − 2 x + 123)
x → −1
50)
Solve: 3cos 2 x − 2 cos x − 7 = 0
51)
⎛
2⎞
sin −1 ⎜⎜ −
⎟⎟
⎝ 2 ⎠
52)
⎛ 3⎞
tan −1 ⎜⎜
⎟⎟
⎝ 3 ⎠
53)
Graph y = 2 cos 5( x + 2π ) − 3
54)
Graph y = − sin
π
3
3
( x − 4) + 1
Precalculus
Final Exam Review Sheet
55)
Write an equation for the graphs shown below:
2π
y
x
−1.0
−2.0
−3.0
−4.0
−5.0
−6.0
−7.0
−8.0
−9.0
10 0
y
3.0
2.0
1.0
2π
x
−1.0
20