Exam
Name
---_._----------~
f ('
'.
e.
Semester Exam - Trigonometry 2012
0'<...<=--\-\(
MULTIPLE CHOICE. Choose the one alternative that best completes
Convert the degree measure
1) 330°
to radians.
Leave answer
or answers
the question.
of if.
as a multiple
1) _-'- __
B) 11i1
A) 1171:
to degrees.
D) 1171:
5
C) 11i1
3
6
12
Convert the radian measure
the statement
Round to the nearest hundredth
if necessary.
2) 1071:
3
A) 601 °
Find the exact circular function
3) cot
B) 599.5°
C) 6000
D) 600.5°
B) Undefined
C)o
D) -1
2)
_
3)
_
value.
71:
A) 1
4)
4) tan 771:
6
C) -
A),J3
2
,J3
371:
5) see
4
A) -2
Use a table or a calculator
13) _
to evaluate
6) cos 0.2806
A) 0.2882
7) cot 0.2119
A) 0.9776
Find the value of s in the interval
8) eos s = 0.41296709
A) 1.28667945
9) cse s = 1.29865617
A) 0.87888309
2,J3
3
C)~2
D)-~
C) 1.041
D) 0.9609
_
6)
_
the function.
13)
0.2769
7)
13)
1.023
C) 4.648
[0,71:/2] that makes the statement
13)
0,42570953
13)
067888309
true.
C) 1.14508679
D) 5.13809851
C) 0.77888309
D) 0.97888309
8)
_
9)
_
10)
C)~4
13) 4
A-I
_
D) 0.2151
Give the amplitude or period as requested.
10) Amplitude of y = -4 sin x
A) 271:
5)
D) -471:
---,
11)
11) Period of y = sin 3x
A) 2n
13)~
0) 3
C)1
3
~l
_
Find the phase shift of the function.
12)y=sin[x+
A)
.!!:...
4
12)
.
down
B) -714 umts
units to the right
O).!!:...
4 units to the left
C) .!!:...
units up
4
13)
13) Y= 5 sin [4x - ~ J
A)
C)
.!!:...
8
B) 71
units to the left
2
units to the right
4n units down
0) 571 units up
Find the exact value of the real number
14) Y = sin-1 [
y.
14)
f]
A)~3
C)71
B) 371
3
4
15)
15) Y= cot-1 (-1)
A)
3n
4
Evaluate the function
16)
_
0) n
4
B) 771
4
requested.
_
\Vrite your answer as a fraction in lowest terms.
16)
A
50
40
B
Find sin A.
.!
A) sin A = 5
13)
5
sin A =4"
C) sin A
=.!3
0) sinA=l
5
Solve the problem.
17) From a boat on the lake, the angle of elevation to the top of a cliff is 29°38'. If the base of the cliff is
655 feet from the boat, how high is the cliff (to the nearest foot)?
A) 383 ft
B) 373 ft
C) 376 ft
0) 386 ft
A-2
17)
_
.ve the triangle.
~
18)
18) B = 34.4°
C = 114.2°
b = 29.50
S) A = 31.4°, a = 27.20, c = 47.63
D) A = 29.4°, a = 49.63, c = 29.20
A) A = 29.4°, a = 47.63, c = 27.20
C) A = 31.4°, a = 29.20, c = 49.63
Solve the problem.
19) To find the distance AB across a river, a distance BC = 1053 m is laid off on one side of the river. It
is found that B = 101.3° and C = 17.0°. Find AS rounded to the nearest meter.
A)309m
Find the area of triangle
20) A = 26.4°
b = 12.3 in.
c= 7.7 in.
B)353m
C)306m
D) 350 m
20)
B) 42.4 in.2
C) 21.1 in.2
D) 44.4 in.2
Solve the problem.
21) Find the area of a triangular-shaped
field with sides of 175.4 m and 226.7m, and the included
between them measuring 79.27° Round to the nearest square meter.
A) 39,068 m2
13)3702 m2
C) 7403 m2
angle
21)
_
D) 19,534 m2
Find the missing parts of the triangle.
22) A = 30.0°
a = 5.13
b = 10.26
22) __
B) B = 90.0°, C = 60.0°, c = 8.89
D) no such triangle
A) B = 60.0°, C = 60.0°, c = 8.89
C) B = 60.0°, C = 90.0°, c = 8.89
23)
23) C = 116.7°
a = 7.50 km
b = 9.80 km
13)c = 17.7 km, A = 28.9°, B = 34.4°
D) c = 14.8 km, A = 26.9°, B = 36.4°
A) No triangle satisfies the given conditions.
C) c = 20.6 km, A = 24.9°,13 = 38.4°
Solve the problem.
24) Two points A and B are on opposite sides of a building. ;\ surveyor chooses a third point C 77 yd
from Band 103 yd from A, with angle ACB measuring 58.9°. How far apart are A and B (to the
nearest yard)?
A) 91 yd
B) 118 yd
C) 109 yd
D)100 yd
A) 106 cm2
19)
ABC with the given parts. Round to the nearest whole number.
A) 19.1 in.2
Find the area of triangle
25) a = 17.4 cm
b = 15.0 cm
c = 13.4 cm
_
24)
ABC with the given parts. Round to the nearest whole number.
25)
13)103 cm2
C) 100 cm2
A-3
D) 97 cm2
_
I'
/tI'dentities
to find the exact value.
26) cos 165°
A)
-J6 +4 -J2
26) __
q -J6 4- -J2
--J6 tj--J2
U)
D)
-J2 4- -J6
Find the exact value of the expression using the provided information.
27) Find cos(s + t) given that cos s =
A) 2-J66 + 1
l,
3
with s in quadrant 1,and sin t =
-J3 +62-J2
13)
_l,2
q -J3 -62-J2
Find the exact value by using a sum or difference identity.
28) tan 75°
A) - -J3 - 2
13) -J3 - 2
with t in quadrant IV.
D) 2-J66 - 1
28) __
q-J3+2
Use trigonometric identities to find the exact value.
29) sin 25° cas 35° + cas 25° sin 35°
A)
-J3
2
29) __
212
13)
q-J33
D)l
2
Use an identity to write the expression as a single trigonometric function or as a single number.
30) 2 cos2 22.5° - 1
A)-J3
13)
3
-J3
q-J2
31) __
+-J2
Solve the equation for the interval [0, 2n).
32) cos2x + 2 cas x + 1 = 0
A)
30) __
·f
Find the exact value by using a half-angle identity.
31) sin 22.5°
A)l~2
2
27)
32)
D)
{2n}
{n}
33) __
Solve the equation in the interval [0°,360°).
34) 4 sin20 = 3
A) {60°,120°, 240°, 300°}
q {2LlO°, 300°}
34) __
13) 0
D) (60°, 120°)
A-4
/
L"'the
complex number
in rectangular
form.
35) __
/",
35) 8(cos
9° ++ iO.4i
sin 9°)
A) 2.8
13)
1.3 + 7.9i
C) -2.8 - O.4i
D) 7.9 + 1.3i
36) __
Find the product. Write the product in rectangular form, using exact values.
37) [7(cos 60° + i sin 60°)] [2(cos 90° + i sin 90°)]
A) 7--.]3- 28 i
Find the following
quotient,
13)
-1'h./3 - 14 i
and write the quotient
37) __
C) -7--.]3 + 7 i
in rectangular
D) 2-]6 - -J2i
form, using exact values.
38) 5(cas 200° + i sin 200°)
4( cas 50° + sin 50°)
38)
i
A) - 5--.]3
+ 5i
8
8
B) - ~2 + --.]3i
2
Find the given power. Write answer
39) (1 - i)10
A) 32 - 32i
in rectangular
C) -2 + 2--.]3i
D) -10 + l0--.j3i
form.
39) __
B) 32
Find all cube roots of the complex number. Leave answers
40) 64( cas 291 ° + i sin 291°)
A) 4 cis 97°,4 cis 217°,4 cis 2170
C) 4 cis 97°,4 cis 217°,4 cis 337"
Give the rectangular coordinates
41) (1,270°)
AHO, 1)
D) -32 + 32i
C) -32i
in trigonometric
form.
40)
B) 4 cis 187°, 4 cis 247°, 4 cis 127°
D) 4 cis 97°, 4 cis 157°, 4 cis 37°
for the point.
41) __
D) (0, -1)
13)(1,0)
42) (6,225°)
A) (-3-J2, -3-J2)
The rectangular
43) (4,4)
coordinates
A) (4,90°)
---
42) __
B) (-371, -371)
of a point are given. Express the point in polar coordinates
13)
(4-J2,4S0)
C) (4-J2, 13S0)
44) (2, -2)
with r::: 0 and 0°::: 8 < 360°.
43) __
D) (4,45°)
44) __
A) (2-J2,45°)
A-5
_
:,wer Key
Lestname: TRIG SEMESTER EXAM 2012
1) B
2) C
3) B
4) B
5) 0
6) 0
7) C
8) C
9) A
10) B
11) B
12) 0
13) A
14) C
15) A
16) A
17) B
18) B
19) 0
20) C
21) 0
22) B
23) 0
24) A
25) 0
26) B
27) B
28) C
29) A
30)
31) C
32) D
0
33) B
34) A
35) 0
36) C
37) C
38) A
39) C
40) C
41) 0
42) A
43) B
44) 0
AJ,