Trigonometry—Departmental Review Sheet Fall 2005
(College Trigonometry, 5th edition. Aufmann, Barker, and Nation. Houghton Mifflin, 2005.)
All work should be shown and all answers should be exact unless stated otherwise. It is fine to leave radicals in
the denominator of a fraction, but they should be reduced. If a problem is given in radians the solution should
also be in radians (the exception is when converting from radians to degrees). The departmental formula sheet
and an acceptable graphing calculator are the only resources allowed for use during the final exam. Each
problem on this review sheet is matched with its corresponding objective in the course outline and the section of
the textbook in which it appears.
[Obj 1, Sec 2.1]
1. Find the complement of (a) 47° (b) 2π/7 Show all your work.
2. Find the supplement of (a) 47° (b) 2π/7 Show all your work.
3. Convert to radians: (a) 68° (b) 3π° Show all your work.
4. Convert to degrees: (a) 3π/8 (b) 45 Show all your work.
5. Find the measure in degrees of the central angle of a circle with radius 10 cm subtended by an arc of 25
cm. Show all your work. Give both the exact answer and the approximate answer rounded to the nearest
thousandth.
6. Find the measure of the intercepted arc of a circle with radius 5 meters and central angle 144°. Give both
the exact answer and the approximate answer rounded to the nearest hundredth. Show all your work.
7. A wheel is rotating at 200 revolutions per minute. Find the angular speed in radians per second.
Show all your work. Give an exact answer.
8. A car with a wheel radius of 14 inches is moving with a speed of 55 mph. Find the angular speed of the
wheel in radians per second. Show all your work. Give your answer to the nearest hundredth.
[Obj 2, Sec 2.2]
9. Find the exact values of the six trigonometric functions of θ for the right triangle shown. θ
Show all your work. 7
10. Let θ be the acute angle of a right triangle with sin θ = ¾. Find the exact values of the other five trig
functions. Show all your work.
11. Find the exact value of 6
tan
4
cos
3
sin
π
π
π
− without using a calculator. Show all your work.
[Obj 3, Sec 2.2]
12. At 3:00 p.m., a boat is 12.5 miles due west of a radar station and traveling at 11 mph in a direction that is
57.3° south of an east-west line. At what time will the boat be closest to the radar station? Give your
answer to the nearest minute. Show all your work.
13. A submarine traveling 9.0 mph is descending at an angle of depression of 5°. How many minutes does it
take the submarine to reach a depth of 80 feet? Give your answer to the nearest hundredth. Show all
your work.
14. Two buildings are 240 feet apart. The angle of elevation from the top of the shorter building to the top of
the other building is 22°. If the shorter building is 80 feet high, how high is the taller building? Give your
answer to the nearest foot. Show all your work.
15. The angle of elevation to the top of a radio antenna on the top of a building is 53.4°. After moving 200
feet closer to the building, the angle of elevation is 64.3°. Find the height of the building if the height of
the antenna is 180 feet. Give your answer to the nearest foot. Show all your work.
[Obj 3, Sec 2.3]
16. State the quadrant in which the terminal side of θ lies if tan θ < 0 and cos θ > 0.
[Obj 2, Sec 2.3]
17. If 3/32sec =
θ
and 2/1sin
−
=
θ
, find the exact value of
θ
cot .
[Obj 1, Sec 2.3]
18. Find the measures of the reference angles. Give exact answers and show all your work.
(a) 254° (b) 18π/7 (c) -312° (d) 10/3
13
