Download Math 1316 t1rf15 - HCC Learning Web

Test 1 Review
Math 1316
06/07/2017
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the
question.
Provide an appropriate response.
1) Find the complement of an angle whose measure is 73°.
2) Find the supplement of an angle whose measure is 74°43′.
Find the angle of least positive measure coterminal with the given angle.
3) -116°
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.
4) (6, 8); Find cos θ.
Use the fundamental identities to find the value of the trigonometric function.
2
5) Find sin θ, given that cos θ = and θ is in quadrant IV.
3
6) Find csc θ, given that cot θ = -
7
and cos θ < 0.
2
Evaluate the function requested. Write your answer as a fraction in lowest terms.
7)
30
18
24
Find sin A.
Without using a calculator, give the exact trigonometric function value with rational denominator.
8) cos 60°
9) cot 45°
Find the reference angle for the given angle.
10) 247.3°
1
Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
11) tan 63°18′
12) sec 57°31′
Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
13) cos θ = 0.22146103
14) sec θ = 2.1411882
Solve the problem.
15) 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 hill's grade (θ > 0 for uphill travel, θ < 0 for downhill travel).
What is the grade resistance (to the nearest pound) of a 2500-lb car traveling downhill on a 6° grade (θ = -6°)?
Find the exact value of the expression.
16) cos 210°
17) tan 690°
18) sin (-2820°)
Find all values of θ, if θ is in the interval [0, 360°) and has the given function value.
1
19) cos θ =
2
20) sin θ = -
1
2
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.
21) Find tan B when a = 24 and c = 25.
22) Find cos A when a = 7 and b = 3.
Use the fundamental identities to find the value of the trigonometric function.
3
23) Find sec θ, given that tan θ = and θ is in quadrant I.
4
24) Find cot θ, given that csc θ = -
7
and θ is in quadrant III.
4
2
Solve the right triangle. If two sides are given, give angles in degrees and minutes.
25)
B = 68°14', b = 17 km
Round side lengths to one decimal place.
Solve the right triangle.
26) A = 14° 14′, c = 269 ft, C = 90°
Round side lengths to two decimal places, if necessary.
Solve the problem.
27) From a boat on the river below a dam, the angle of elevation to the top of the dam is 22°56'. If the dam is 1688
feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?
28) A fire is sighted due west of lookout A. The bearing of the fire from lookout B, 12.6 miles due south of A, is N
40°50'W. How far is the fire from B (to the nearest tenth of a mile)?
29) An airplane travels at 145 km/h for 5 hr in a direction of 97° from a local airport. At the end of this time, how
far east of the airport is the plane (to the nearest kilometer)?
30) Find h as indicated in the figure. Round to the nearest foot.
24.7°
56.9°
110 ft
31) Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he
measures the angle of elevation to the top of the mountain and finds it to be 22° 39′. He then drives 1 mile
(1 mile = 5280 ft) more and measures the angle of elevation to be 33° 58′. Find the height of the mountain to the
nearest foot.
3
Answer Key
Testname: MATH 1316 T1RF17
1) 17°
2) 105°17′
3) 244°
4)
3
5
5
3
5) -
53
2
6)
7) sin A =
8)
4
5
1
2
9) 1
10) 67.3°
11) 1.9882787
12) 1.8620093
13) 77.2051392°
14) 62.1582940°
15) -261 lb
16) -
3
2
17) -
3
3
18)
3
2
19) 60° and 300°
20) 210° and 330°
21)
7
24
22)
3 58
58
23)
5
4
24)
33
4
25) A = 21°46'; c = 18.3 km; a = 6.8 km
26) B = 75° 46′, a = 66.14 ft, b = 260.74 ft
27) 3990 ft
28) 16.7 mi
29) 720 km
30) 72 ft
31) 5789 ft
4