Download math 1316 review 1

MATH 1316
REVIEW 1
L F Thomas - Instructor
Provide an appropriate response.
1) Find the supplement of an angle whose measure is 37°.
2) Find the complement of an angle whose measure is 38°18 .
Find the measure of each angle in the problem.
3)
4)
Perform the calculation.
5) 90° - 54°52
6) 92°24 - 34°44
Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
7) 131°57 32
8) 68°40 8
Convert the angle to degrees, minutes, and seconds.
9) 40.78°
Find the angle of least positive measure coterminal with the given angle.
10) -116°
11) 500°
Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
12) 179°
1
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.
13) 65°
Solve the problem.
14) A wheel makes 372 revolutions per minute. How many revolutions does it make per second?
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 .
15) (6, 8); Find cos .
16) (18, 24); Find csc .
17) (6, 5); Find tan .
Evaluate the expression.
18) tan(-180°)
19) cot2 90° - sec 180°
20) 4 tan 360° + 5 csc 270°
21) rcot 270° + 6 cos 180° + 5 sec2 360°
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.
22) cos , given that sec = -4
6
7
23) tan , given that cot
=-
24) csc , given that sin
= -0.4271
Use the fundamental identities to find the value of the trigonometric function.
2
25) Find csc , given that sin = - and is in quadrant IV.
3
26) Find tan , given that sin
=
27) Find cot , given that tan
=
3
and
4
7
and
3
is in quadrant II.
is in quadrant III.
2
Evaluate the function requested. Write your answer as a fraction in lowest terms.
28)
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.
29) Find sin A when b = 27 and c = 45
30) Find tan B when a = 24 and c = 25.
Without using a calculator, give the exact trigonometric function value with rational denominator.
31) cos 30°
32) sin 60°
33) tan 45°
Solve the problem.
34) Find the exact value of x in the figure.
14
Evaluate.
35) 3 tan2 60° + 3 sin2 30° - cos2 360°
36) 5 sin2 240° + csc2 150° - sec2 30°
37) 4 sin2 60° + csc2 30° - sec2 150°
3
Solve the problem.
38) To measure the width of a river, a surveyor starts at point A on one bank and walks 70 feet down the river to
point B. He then measures the angle ABC to be 24°38'12''. Estimate the width of the river to the nearest foot. See
the figure below.
C
A
70 ft
B
39) 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)?
40) A boat sails for 5 hours at 25 mph in a direction 164°23'. How far south has it sailed (to the nearest mile)?
41) 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)?
42) The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin , where W is
the weight of the car and is the angle of the hill's grade ( > 0 for uphill travel, < 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.
4
Answer Key
Testname: REVIEW 1
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
143°
51°42
45° and 135°
70° and 20°
35°8
57°40
131.96°
68.67°
40°46 48
244°
140°
179° + n · 360°
425° and -295°
14) 6.2 revolutions per second
3
15)
5
16)
5
4
17)
5
6
18)
19)
20)
21)
0
1
-5
-1
1
22) 4
23) -
7
6
24) -2.341
3
25) 2
26) 27)
3 7
7
3 7
7
28) tan A =
29)
4
5
30)
7
24
5
12
5
Answer Key
Testname: REVIEW 1
31)
3
2
32)
3
2
33) 1
34) 7 6
35
35)
4
36)
77
12
37)
17
3
38)
39)
40)
41)
42)
32 ft
16.7 mi
120 mi
720 km
4000 lb
6