Download Math 113 Test I Practice Problems spring 11.tst

Math 113 Test I Practice Problems
Sections 4.1-4.6
The given angle is in standard position. Determine the
quadrant in which the angle lies.
1) 262°
Convert the angle in radians to degrees. Round to two
decimal places.
14) -2.54 radians
2) -52°
Find a positive angle less than 360° that is coterminal with
the given angle.
15) -234°
3) -342°
Classify the angle as acute, right, obtuse, or straight.
4)
16)
5π
2
17) - Find the length of the arc on a circle of radius r
intercepted by a central angle θ. Round answer to two
decimal places.
18) r = 50 inches, θ = 20°
5)
Solve the problem.
19) The minute hand of a clock is 4 inches long.
How far does the tip of the minute hand move
in 15 minutes? If necessary, round the answer
to two decimal places.
6) 114°
Find the radian measure of the central angle of a circle of
radius r that intercepts an arc of length s.
7) r = 6 inches, s = 30 inches
20) To approximate the speed of a river, a circular
paddle wheel with radius 0.55 feet is lowered
into the water. If the current causes the wheel
to rotate at a speed of 9 revolutions per
minute, what is the speed of the current?
Express the answer in miles per hour rounded
to two decimal places, if necessary.
8) r = 1 meter, s = 200 centimeters
Convert the angle in degrees to radians. Express answer as
a multiple of π.
9) 54°
21) What is the domain of the cosine function?
10) - 480°
22) What is the range of the cosine function?
Convert the angle in radians to degrees.
π
11) - 5
12)
7π
10
Find the exact value.
π
23) sec 4
9π
4
Find the exact value of the expression if θ = 45°. Do not
use a calculator.
24) (cos θ)2
Convert the angle in degrees to radians. Round to two
decimal places.
13) 194°
25) 4 cos θ
1
26)
sin θ
4
38) cos Find the exact value.
π
27) sin (- )
6
28) sin - Use a calculator to find the value of the trigonometric
function to four decimal places.
39) sin 0.4
40) cos 0.3
π
4
41) cot π
12
42) sec π
10
29) sin (-120°)
30) cot - 35π
6
π
6
Two sides of a right triangle ABC (C is the right angle) are
given. Find the indicated trigonometric function of the
given angle. Give an exact answer with a rational
denominator.
43)
Sin t and cos t are given. Use identities to find the
indicated value. Where necessary, rationalize
denominators.
5
-2 6
. Find csc t.
31) sin t = , cos t = 7
7
3 5
2
. Find tan t.
32) sin t = - , cos t = 7
7
9
8
π
0 ≤ t < and sin t is given. Use the Pythagorean identity
2
Find cos θ.
sin2 t + cos2 t = 1 to find cos t.
1
33) sin t = 4
Use the given triangles to evaluate the expression.
Rationalize all denominators.
Use an identity to find the value of the expression. Do not
use a calculator.
34) sin 1.7 csc 1.7
Find the exact value of the trigonometric function. Do not
use a calculator.
5π
35) tan 4
36) tan - 37) cos 5π
4
π
π
π
44) sin csc + tan 3
3
3
14π
3
2
Find the reference angle for the given angle.
57) 96°
Find a cofunction with the same value as the given
expression.
π
45) tan 12
58) -53.2°
46) csc 80°
Use reference angles to find the exact value of the
expression. Do not use a calculator.
-2π
59) sin 3
Solve the problem.
47) A building 300 feet tall casts a 60 foot long
shadow. If a person stands at the end of the
shadow and looks up to the top of the
building, what is the angle of the personʹs eyes
to the top of the building (to the nearest
hundredth of a degree)? (Assume the personʹs
eyes are 4 feet above ground level.)
60) tan 930°
Determine the amplitude or period as requested.
61) Amplitude of y = -3 sin x
62) Period of y = sin 3x
Use a calculator to find the value of the acute angle θ to
the nearest degree.
48) cos θ = 0.2286
Determine the phase shift of the function.
1
63) y = sin (4x + π)
4
Use a calculator to find the value of the acute angle θ in
radians, rounded to three decimal places.
49) tan θ = 13.2894
Graph the function.
π
64) y = 4 sin (x + )
3
A point on the terminal side of angle θ is given. Find the
exact value of the indicated trigonometric function of θ.
50) (9, 12) Find cos θ.
y
3
51) (-3, 4) Find cot θ.
Evaluate the trigonometric function at the quadrantal
angle, or state that the expression is undefined.
52) tan π
53) cot -π
π
2
-3
3π
2
Let θ be an angle in standard position. Name the quadrant
in which the angle θ lies.
54) tan θ < 0, sin θ < 0
Determine the phase shift of the function.
65) y = 3 cos (2πx + 3)
Find the exact value of the indicated trigonometric
function of θ.
7
55) sec θ = , θ in quadrant IV
Find tan θ.
4
7
56) csc θ = - , θ in quadrant III
4
-π
2
Find cot θ.
3
π
x
69) y = csc x
Use a vertical shift to graph the function.
1
66) y = -4 sin x + 2
2
6
3
y
y
4
-2π
2
-2π
-π
π
2π
-π
π
2π
π
2π
x
x
-2
-3
-4
70) y = sec x
-6
3
y
Graph the function.
π
67) y = tan (x + )
2
y
2
-2π
-π
1
-3
-π
2
π
2
3π
2
π
2π
x
-1
-2
68) y = cot x
y
2
1
-π
π
2
-π
2
π
3π
2
2π
5π
2
3π
x
-1
-2
4
x
Answer Key
Testname: MATH 113 TEST I PRACTICE PROBLEMS SPRING 11
1)
2)
3)
4)
5)
6)
7)
8)
Quadrant III
Quadrant IV
Quadrant I
acute
straight
obtuse
5 radians
2 radians
3π
9)
radians
10
10) - 29) - 30) - 3
7
31)
5
8π
radians
3
5π 4π π
5π
- 2π = - = 2
2
2
2
17)
13π
10
15
4
3
2
43) cos θ = 44) sin .55
.55
. v = rω = × (18π
5280
5280
× 60) ≈ 0.35 miles per hour or 8 145
145
π opp
3
π
2
π opp
= , csc = , tan = = 3 .
=
3 hyp
3
3
adj
2
3
Substitute those values into the problem and you
should get the answer which is 1 + 3
5π
45) cot 12
2π ≈ 6.28 inches
9 rev 2(.55)π ft.
·
·
1 rev
1 min
46) sec 10°
47) 78.54°
48) 77°
49) 1.496 radians
3
50)
5
60 min 1 mile
·
= .35 miles/hour
1 hour 5280 ft.
21) all real numbers
22) all real numbers from -1 to 1, inclusive
23) 2
1
24)
2
51) - 3
4
52) 0
53) 0
54) quadrant IV
33
55) - 4
25) 2 2
2
26)
8
28) -
33)
39) 0.3894
40) 0.9553
41) 3.7320
42) 1.0515
You must change 20∘ to radian measure first.
17.45 inches
1 2π 2π π
15
π
19) s = rω, r = 4, ω = ·2π = · = = . s = 4· =
4 1
4 2
60
2
27) - -2 5
15
38)
18) s = r θ
20) ω = 9 × 2π = 18π × 60, r = 32)
34) 1
35) 1
36) -1
1
37) - 2
11) -36°
12) 405°
13) 3.39 radians
14) -145.53°
15) -234 ∘ + 360 ∘ =126°
16)
3
2
1
2
56)
2
2
33
4
57) 84°
58) 53.2°
5
Answer Key
Testname: MATH 113 TEST I PRACTICE PROBLEMS SPRING 11
59) - 60)
67)
3
2
y
2
3
3
1
61) 3
2π
62)
3
π
2
-π
2
π
63) units to the left
4
3π
2
π
2π
x
-1
64)
-2
y
68)
3
y
2
-π
π
2
-π
2
π
x
1
-3
-π
π
2
-π
2
π
3π
2
2π
5π
2
3π
-1
3
65)
units to the left
2π
-2
66)
6
y
69)
4
3
y
2
-2π
-π
π
2π
x
-2
-2π
-4
-π
π
-6
-3
6
2π
x
x
Answer Key
Testname: MATH 113 TEST I PRACTICE PROBLEMS SPRING 11
70)
3
-2π
-π
y
π
2π
x
-3
7