Download E. McGann LA Mission College Math 125 Fall 2014 Test #1

E. McGann
LA Mission College
Math 125
Fall 2014
Test #1 --> chapters 3, 4, & 5
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate response.
1) Find the complement of an angle whose measure is 71°.
A) 19°
B) 109°
C) 161°
D) 71°
Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
2)
A) Right, isosceles
B) Obtuse, equilateral
C) Obtuse, scalene
D) Acute, equilateral
Provide an appropriate response.
3) Find the supplement of an angle whose measure is 60°.
A) 240°
B) 150°
C) 30°
D) 120°
C) 100° and 80°
D) 200° and 160°
Find the measure of each angle in the problem.
4)
A) 50° and 40°
B) 95° and 85°
5) Complementary angles with measures 3x and 6x - 18 degrees
A) 66° and 114°
B) 36° and 54°
C) 12° and 78°
D) 38° and 52°
6) Supplementary angles with measures 2x + 7 and 3x - 2 degrees
A) 57° and 123°
B) 77° and 103°
C) 67° and 113°
D) 87° and 93°
Find the angle of least positive measure coterminal with the given angle.
7) 652°
A) 292°
B) 326°
C) 282°
1
D) 472°
Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
8) -180°
A) -180° + n · 360°
B) -180° - n · 180°
C) -180° + n · 180°
D) -180° + 2n · 360°
9) 98°
A) 98° + n · 360°
B) 98° + n · 90°
C) 98° + n · 720°
D) 98° + n · 180°
Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
10) 50°
A)
B)
410° and -310°
230° and -130°
C) 230° and -130°
11) 115°
A)
D)
295° and -65°
B)
C) 475° and -245°
410° and -310°
475° and -245°
D) 295° and -65°
Use the properties of angle measures to find the measure of each marked angle.
12)
a = (2x + 8)°
b = (4x - 62)°
A) 35°, 35°
B) 55°, 55°
C) -16°, -16°
2
D) 78°, 78°
13)
a = (x + 18)°
b = (x + 118)°
A) 11°, 22°, 147°
B) 22°, 29°, 129°
C) 11°, 22°, 57°
D) 79°, 79°, 22°
B) 3°, 177°
C) 87°, 93°
D) °, 172°
14) Lines m and n are parallel.
a = (4x + 10)°
b = (5x + 143)°
A) 22°, 158°
Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
15)
A) Obtuse, equilateral
B) Acute, equilateral
C) Obtuse, isosceles
D) Acute, scalene
Find the angle of least positive measure coterminal with the given angle.
16) -116°
A) 116°
B) 424°
C) 244°
D)
°
The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
17) AC
A) Cannot be determined
B) SR
C) RT
D) ST
3
The triangles are similar. Find the missing side, angle or value of the variable.
18) R
a = 15 cm
b = 111°
A) 111°
B) 59°
C) 15 cm
D) 10°
B) x = 10
C) x = 15
D) x = 5
19)
a = 13
b = 12
c=5
d = 26
e = 24
A) x = 7
Solve the problem. Round answers to the nearest tenth if necessary.
20) A tree casts a shadow 38 m long. At the same time, the shadow cast by a 37-centimeter-tall statue is 75 cm
long. Find the height of the tree.
A) 75.5 m
B) 17.2 m
C) 18.7 m
D) 77.0 m
4
Sketch an angle in standard position such that
side of .
21) (3, 6)
has the least positive measure and the given point is on the terminal
A)
B)
C)
D)
5
22) (-5, 3)
A)
B)
C)
D)
Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the
indicated trig function for .
23) (12, 16); Find sin .
A) 3
B) 4
C) 3
D) 4
5
3
4
5
24) (15, 20); Find cos .
A) 4
5
B) 4
C) 3
3
5
6
D) 3
4
An equation of the terminal side of an angle in standard position is given along with a restriction on x. Find the
indicated trigonometric function value of . Do not use a calculator.
25) y = 3x, x 0; Find tan .
A) 1
B) 10
C) 3
D) 3 10
3
10
10
Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the
indicated trig function for .
26) (-7, 8); Find cot .
A) - 7
B) - 7
C) - 8
D) 8
8
11
7
11
Place your calculator in degree modes.
27) For what angle T is cos T 0.866? (Assume 0° T
A) 0.866°
B) 28.65°
90°.)
C) 60°
D) 30°
C) 0.766°
D) 40°
C) 1
D) 0
C) Undefined
D)
Solve for T
28) For what angle T is cos T 0.766? (Assume 0° T 90°.)
A) 50°
B) 36.832°
Evaluate the expression.
29) cot 450°
A) Undefined
B)
2
2
30) cot 270°
A) -1
B)
2
2
If n is an integer, n · 180° represents an integer multiple of 180°, and (2n + 1) · 90° represents an odd integer multiple of
90°. Decide whether the expression is equal to 0, 1, -1, or is undefined.
31) tan(n · 180°)
A) -1
B) Undefined
C) 0
D) 1
If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or
negative.
32) III, x
y
A) Negative
B) Positive
33) IV, x
y
A) Negative
B) Positive
7
Evaluate the expression.
34) sin2 360° + cos2 360°
A) 2
35) cot2 90° - sec 180°
A) 0
B) 1
C) 3
D) 2
B) 1
C) -1
D) 2
Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
36) cos , given that sec = -7
A) 1
B) - 1
C) - 1
D) 1
7
7
6
6
37) tan , given that cot = - 10
11
A) 21
B) - 11
11
C) 11
10
38) csc , given that sin =
10
D) - 10
11
11
6
A) 11 11
B)
6
11
11
C)
11
6
D) 6 11
11
Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
39) cos (500°) and tan (500°)
A) negative and positive
B) negative and negative
C) positive and negative
Identify the quadrant for the angle
40) tan > 0 and sin < 0
A) Quadrant I
41) cos < 0 and csc < 0
A) Quadrant II
D) positive and positive
satisfying the following conditions.
B) Quadrant IV
C) Quadrant III
D) Quadrant II
B) Quadrant III
C) Quadrant I
D) Quadrant IV
Decide whether the statement is possible or impossible for an angle .
42) sin = 7.37
A) Impossible
B) Possible
43) tan = -1.36
A) Possible
B) Impossible
8
Use the fundamental identities to find the value of the trigonometric function.
44) Find csc , given that sin = - 2 and is in quadrant IV.
3
A) 3 7
7
B) 5
C) -
4
7
9
D) - 3
2
45) Find tan , given that sin = 3 and is in quadrant II.
4
A) -
7
9
C) - 3 7
B) 5
4
7
9
D) - 3
2
Answer Key
Testname: CHAPTER 1 QUIZ 1 REVIEW WITH ANSWERS
1) A
2) C
3) D
4) C
5) B
6) B
7) A
8) A
9) A
10) B
11) C
12) D
13) B
14) A
15) B
16) C
17) B
18) A
19) B
20) C
21) A
22) C
23) D
24) C
25) C
26) A
27) D
28) D
29) D
30) B
31) C
32) B
33) A
34) B
35) B
36) B
37) B
38) D
39) B
40) C
41) B
42) A
10
Answer Key
Testname: CHAPTER 1 QUIZ 1 REVIEW WITH ANSWERS
43) A
44) D
45) C
11