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Trigonometry
Final Exam Review Sheet . All work must be shown. Just having answers is not sufficient to receive full
credit on the review.
1.
Solve the equation if possible: 3x – 2(x + 5) = 10
2.
Solve the equation if possible: x² – 12 x + 30 = 0
3.
Solve the equation if possible: 12t³ – 84t² + 120t = 0
4.
Find the distance between the following two points: (-1, 4) and (2, 0)
5.
Find the midpoint between the following two points (-2, 2) and (3, -10)
6.
Determine the center and the radius of the following circle:
x² + y² – 20x – 10y + 100 = 0
7.
Sketch the graph of y = 8 – x
8.
Determine the domain of f(x) =  x + 2
9.
Find the inverse of the function f(x) = x³ + 2
10.
Convert 5 to degrees. Be sure to round your answer to two decimal places.
7
11.
Convert 8415’ to radians. Be sure to round your answer to 4 decimal places.
12.
Find the reference angle of 640
13.
Evaluate the trigonometric function without the aid of a calculator: sin (5)
3
14.
Find the value of csc 270
15.
Given that the cos 29 = .8746, evaluate the cos 151
16.
Find the secant of 11 without the aid of a calculator
4
17.
Change 320 to radians in terms of 
18.
Change  to degrees
9
19.
Write an algebraic expression for sec [arcsin (x – 1)]
20.
Find the five remaining functions given that sin  =
21.
Find the period, amplitude, and five key points of y = 3 cos ( x +  ). Then sketch the graph.
22.
Sketch y = sin x + 2
11
and cos  < 0
61
23.
Sketch y = 2 tan x
24.
Sketch y = 3csc (x –  )
2
25.
Sketch y = –2sec x
26.
Sketch y = cot (x –  )
4
27.
Sketch y = log3 x
28.
Evaluate arccos .28
29.
Evaluate arctan (-1)
30.
Find the exact value of cos(arctan 2) without the aid of a calculator.
31.
Verify the identity.
32.
Solve 3tan² x – 1 = 0 on the interval [0, 2)
33.
Solve cot x cos² x = 2 cot x on the interval [0, 2)
34.
Evaluate ln e³
35.
Evaluate log27 9
csc x – sin x = cos x cot x
36.
A 20 foot ladder leaning against the side of a house makes a 75 with the ground. How far up the
side of the house does the ladder reach?
37.
From a 150-foot observation tower on the coast, a Coast Guard officer sights a boat in difficulty.
The angel of depression of the boat is 4. How far is the boat from the shoreline?
38.
An amateur radio operator erects a 75-foot vertical tower for his antenna. Find the angle of elevation
to the top of the tower at a point on level ground 50 feet from the base.
39.
Find the remaining sides and angles of the triangle if
A = 24.3, C = 54.6, and c = 2.68
40.
Find the remaining sides and angles of the triangle if a = 9, b = 12, c = 15
41.
Use Heron’s formula to find the area of a triangle with sides of
a = 5, b = 7, c = 10
42.
Find the trigonometric form of -4 + 4i
43.
2
Find the standard form of 2(cos2 + i sin
)
3
3
44.
Use DeMoivre’s Theorem to find [5(cos 20 + i sin 20)]³
Review Sheet Answers
1.
20
2.
6 ± 6
3.
0, 2, 5
4.
5
5.
(.5 , -4)
6.
center ( 10, 5) radius = 5
7.
see graph
8.
x  -2
9.
f-1(x) = ³ x –2
10.
128.57˚
11.
1.4704
12.
80
13.
3
2
14.
-1
15.
-.8746
16.
- 2
17.
16
9
18.
20
19.
 - x² + 2x
-x² + 2x
20.
cos  = - 60 / 61
tan  = -11/60
csc  = 61/11
sec  = - 61/60
cot  = - 60/11
21.
amp. = 3
per. = 2
key points: (-, 3) ( -/2 , 0) ( 0, -3 ) (/2, 0) (, 3)
22.
See graph
23.
See graph
24.
See graph
25.
See graph
26.
See graph
27.
See graph
28.
1.29 radians or 73.7
29.
–/4
30.
5/5
31.
answers may vary
32.
/6 and 5/6 and 7/6 and 11/6
33.
/2 and 3/2
34.
2/3
35.
19.32 feet
36.
2145 feet
37.
56.3
38.
B = 101.1, a 1.35 , b  3.23
39.
A36.9, B 53.1 , C 90
40.
16.25 sq. units
41. 42 cis 135
42. –1 + i3
43. 125 + 125i3
2
2