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Practice Exam 1
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Convert the angle to a decimal in degrees. Round the answer to two decimal places.
1) 13°11'5''
A) 13.14°
B) 13.24°
C) 13.19°
2) 182°11'59''
A) 182.21°
B) 182.16°
C) 182.26°
Convert the angle to D° M' S'' form. Round the answer to the nearest second.
3) 94.78°
A) 94°46'48''
B) 94°46'78''
C) 94°46'36''
D) 13.18°
D) 182.20°
D) 94°46'54''
1)
2)
3)
If s denotes the length of the arc of a circle of radius r subtended by a central angle , find the missing quantity.
4) r = 2.29 centimeters, = 5 radians, s = ?
4)
A) 11.5 cm
B) 12.5 cm
C) 13.5 cm
D) 10.5 cm
5) r = 13.9 inches,
A) 36.7 in.
6) r =
= 150°, s = ?
B) 36.5 in.
1
feet, s = 6 feet,
4
A) 24°
C) 36.6 in.
D) 36.4 in.
=?
6)
B)
3
radians
2
C) 24 radians
D)
3
°
2
Convert the angle in degrees to radians. Express the answer as multiple of .
7) 36°
A)
B)
4
C)
7
7)
D)
5
6
8) -90°
A) -
8)
4
B) -
C) -
2
8
D) -
3
Convert the angle in radians to degrees.
12
9)
9
A) 241°
10) -
5)
9)
B) 242°
C) 240°
D) 239°
5
6
A) -150°
10)
B) -149°
C) -152°
1
D) -151°
If A denotes the area of the sector of a circle of radius r formed by the central angle , find the missing quantity. If
necessary, round the answer to two decimal places.
11) r = 20 inches,
=
A) 104.67 in2
6
radians, A = ?
11)
B) 10.47 in2
12) r = 4 feet, A = 47 square feet, = ?
A) 2.94 radians
B) 752 radians
13)
=
6
C) 5.23 in2
D) 209.33 in2
C) 5.88 radians
D) 376 radians
radians, A = 33 square meters, r = ?
A) 8.64 m
12)
13)
B) 34.56 m
C) 2.94 m
Find the value of the indicated trigonometric function of the angle
denominator.
14)
D) 11.23 m
in the figure. Give an exact answer with a rational
14)
7
4
Find sin .
A) sin
65
7
=
B) sin
=
4 65
65
C) sin
=
7 65
65
D) sin
=
15)
65
4
15)
7
Find sin .
33
A)
7
4
B)
4
7
C)
4 33
33
D)
7 33
33
Use identities to find the exact value of the indicated trigonometric function of the acute angle .
2 2
1
, cos =
Find tan .
16) sin =
3
3
A) 2 2
B)
2
4
C)
2
3 2
4
D) 3
16)
17) sin
A)
=
1
, cos
4
=
4 15
15
15
4
Find cot .
B)
17)
15
15
C) 4
15
D)
Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle .
5
Find tan .
18) sin =
18)
13
A)
19) sin
A)
20) cos
A)
12
5
=
4
5
4
3
=
B)
3
4
C)
13
12
D)
13
5
Find csc .
B)
3
5
5
12
19)
5
4
C)
3
4
D)
5
3
Find sec .
B)
20)
4
3
C)
5
3
D)
5
4
Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not
use a calculator.
sec 50°
21) 21)
csc 40°
A) 0
22) csc2 60° - tan2 30°
A) 1
B) -1
C) 1
D) undefined
B) -1
C) 0
D) 2
Solve the problem.
23) A radio transmission tower is 170 feet tall. How long should a guy wire be if it is to be attached 15
feet from the top and is to make an angle of 30° with the ground? Give your answer to the nearest
tenth of a foot.
A) 196.3 ft
B) 340.0 ft
C) 310.0 ft
D) 179.0 ft
24) A building 230 feet tall casts a 100 foot long shadow. If a person looks down from the top of the
building, what is the measure of the angle between the end of the shadow and the vertical side of
the building (to the nearest degree)? (Assume the person's eyes are level with the top of the
building.)
A) 67°
B) 26°
C) 64°
D) 23°
22)
23)
24)
A point on the terminal side of angle is given. Find the exact value of the indicated trigonometric function.
25) (12, 16)
Find sin .
25)
4
4
3
3
A)
B)
C)
D)
5
3
4
5
3
26) (3, 4)
Find cos .
4
A)
3
3
B)
5
4
C)
5
26)
3
D)
4
Use a coterminal angle to find the exact value of the expression. Do not use a calculator.
27) cos 405°
2
2
1
1
A)
B) C)
D) 2
2
2
2
27)
28) cot -660°
28)
A) - 3
B)
3
2
C)
3
D)
3
3
Use the reference angle to find the exact value of the expression. Do not use a calculator.
29) sin 495°
2
2
1
1
A) B) C)
D)
2
2
2
2
29)
30) tan 750°
30)
3
B)
3
3
A)
3
C)
2
D) - 3
31) csc 600°
31)
A) - 2
B) -
2 3
3
C) - 3
D) -
1
2
Find the exact value of the indicated trigonometric function of .
2
Find sin .
32) cos = , tan < 0
9
A) - 77
33) sec
=
A) -
34) sin
A)
5
,
2
B) -
in quadrant IV
5
2
=5
2
C) -
9
2
D) -
77
2
Find tan .
B) -
2
, tan
5
77
9
32)
>0
33)
21
5
C) -
21
D) -
21
2
Find sec .
B) -
34)
2 21
21
C) -
4
21
5
D) -
5 21
21
The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function.
5
11
Find sin t.
35) ,
35)
6 6
11
5
A)
36)
3
7
,
4 4
A)
3 7
7
B)
5 11
11
11
6
C)
D)
5
6
Find tan t.
36)
B)
7
4
7
3
C)
D)
4
3
Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
37) sin (-60°)
3
3
1
1
A)
B)
C) D) 2
2
2
2
38) cos (-30°)
3
A) 2
39) sec (-30°)
2 3
A) 3
37)
38)
B)
3
2
C)
1
2
D) -
1
2
39)
2 3
C)
3
B) -2
D) 2
Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.
40) sin 495°
40)
2
2
1
1
A)
B) C) D)
2
2
2
2
41) tan 570°
3
A)
3
41)
B)
3
C)
3
2
D) - 3
42) csc 960°
A) - 2
42)
B) -
1
2
C) -
5
2 3
3
D) - 3
Answer Key
Testname: MAC1114_PE1
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
D
D
A
A
D
C
C
B
C
A
A
C
D
C
B
A
D
B
B
C
B
A
C
D
A
B
A
D
C
B
B
B
D
D
C
C
A
B
B
D
A
C
6