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Exam 1 Review Math1316
Provide an appropriate response.
1) Find the supplement of an angle whose measure is 74°43′.
2) Find the complement of an angle whose measure is 39°16′50′′ .
Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
3) 131°57′32′′
Convert the angle to degrees, minutes, and seconds.
4) 47.46°
Find the angle of least positive measure coterminal with the given angle.
5) 877°
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.
6) 65°
Solve the problem.
7) A wheel is rotating 900 times per minute. Through how many degrees does a point on the edge of the wheel
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move in seconds?
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Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the
indicated trig function for θ.
8) (-20, 48); Find sin θ.
Evaluate the expression.
9) sec(-90°)
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.
r
10) III, x
Evaluate the expression.
11) cos 0° - 8 sin 90°
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.
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12) csc θ, given that sin θ = 7
13) tan θ, given that cot θ = 5
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Identify the quadrant for the angle θ satisfying the following conditions.
14) cot θ < 0 and cos θ > 0
Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
15) csc (608°) and cot (608°)
Decide whether the statement is possible or impossible for an angle θ.
16) sec θ = -0.41
Use the fundamental identities to find the value of the trigonometric function.
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17) Find sin θ, given that cos θ = and θ is in quadrant IV.
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18) Find cot θ, given that csc θ = - and θ is in quadrant III.
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Evaluate the function requested. Write your answer as a fraction in lowest terms.
19)
13
5
12
Find tan A.
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length
using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle.
Rationalize the denominator if applicable.
20) Find csc A when b = 40 and c = 85
Without using a calculator, give the exact trigonometric function value with rational denominator.
21) sin 60°
Solve the problem.
22) Find the exact value of x in the figure.
22
2
Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle.
23) cos 48°
Find a solution for the equation. Assume that all angles are acute angles.
24) tan(3α + 32°) = cot(α + 36°)
Decide whether the statement is true or false.
25) cos 72° ≤ cos 59°
Solve the problem for the given information.
26) Find the equation of a line passing through the origin and making a 45° angle with the positive x-axis.
Find the reference angle for the given angle.
27) 247.3°
Find the exact value of the expression.
28) tan 300°
Evaluate.
29) 3 tan2 60° + 3 sin2 30° - cos2 360°
Find the sign of the following.
θ
30) sin , given that θ is in the interval (180°, 270°).
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Find all values of θ, if θ is in the interval [0, 360°) and has the given function value.
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31) sin θ = 2
32) sec θ = - 2
Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
33) cos 366°19′
Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
34) cos θ = 0.22146103
Solve the problem.
35) The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin θ, where W is
the weight of the car and θ is the angle of the hillʹs grade (θ > 0 for uphill travel, θ < 0 for downhill travel). Find
the weight of the car (to the nearest pound) that is traveling on a -2.2° downhill grade and which has a grade
resistance of -153.55 lb.
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Solve the right triangle. If two sides are given, give angles in degrees and minutes.
36)
A = 33.3°, b = 3.8 m
Round side lengths to one decimal place.
Solve the problem.
37) On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 40 meters long and
the tree is 32 meters tall, how long is the shadow?
38) A 39-foot ladder is leaning against the side of a building. If the ladder makes an angle of 23° 41′ with the side
of the building, how far up from the ground does the ladder make contact with the building? Round your
answer to the hundredths place when necessary.
39) A ship travels 58 km on a bearing of 21°, and then travels on a bearing of 111° for 123 km. Find the distance
from the starting point to the end of the trip, to the nearest kilometer.
Solve the right triangle. If two sides are given, give angles in degrees and minutes.
40)
a = 20.3 cm, b = 20.8 cm
Round the missing side length to one decimal place.
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Answer Key
Testname: EXAM1 REVIEW
1)
2)
3)
4)
5)
6)
105°17′
50°43′10′′
131.96°
47°27′36′′
157°
425° and -295°
7) 1800°
12
8)
13
9) Undefined
10) Negative
11) -7
12) 7
6 5
13)
5
14) Quadrant IV
15) negative and positive
16) Impossible
5
17) - 3
18)
33
4
19) tan A = 20)
21)
5
12
17
15
3
2
22) 11 3
23) sin 42°
24) 5.5°
25) True
26) y = x
27) 67.3°
28) - 3
35
29)
4
30) positive
31) 60° and 120°
32) 135° and 225°
33) 0.993929
34) 77.2051392°
35) 4000 lb
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Answer Key
Testname: EXAM1 REVIEW
36) B = 56.7°; a = 2.5 m; c = 4.5 m
37) 24 m
38) 35.72 ft
39) 136 km
40) A = 44°18ʹ; B = 45°42ʹ; c = 29.1 cm
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