Math 8
CHAPTER 2 QUIZ
Name:_______________________________________________
Complete, organized, and correct work, using the methods taught in class and including correct use of symbols, is required
to receive full credit. Partial or no credit will be given when work is missing. Each problem is worth 5 points.
SHOW ALL WORK . DO NOT ROUND ANSWERS UNLESS INSTRUCTED TO DO SO. Express answers in lowest
terms. Simplify all radicals.
time: 30 minutes
Convert the angle to a decimal in degrees. Round the answer to two decimal places.
1) 84°48'48''
84° + 48 ·
1°
1°
+ 48 ·
60
3600
84° + .8 + .013
84..81
Convert the angle to D° M' S'' form. Round the answer to the nearest second.
2) 64.38°
64° + .38° ·
60
1°
64° + 22 + .8 ·
= 64° + 22.8
60
1
= 64° + 22 + 48
64°22 48
If s denotes the length of the arc of a circle of radius r subtended by a central angle , find the missing quantity. Round
to the nearest tenth, if necessary.
3) r = 15.7 inches, = 210°, s = ?
s = 15.7in 210° ·
s
180°
57.5in
Solve the problem.
4) A car is traveling at 27 mph. If its tires have a diameter of 28 inches, how fast are the car's tires turning? Express
the answer in revolutions per minute. If necessary, round to two decimal places.
27mi
1hr
5280ft 12in
1rev
·
·
·
·
hr
60min
1mi
1ft
28 in
324.29rpm
If A denotes the area of the sector of a circle of radius r formed by the central angle , find the missing quantity. If
necessary, round the answer to two decimal places.
5) r = 3 inches,
A=
=
1
3in 2
2
4
4
radians, A = ?
3.53in2
In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value
of the indicated trigonometric function of t.
5
2 6
)
6) ( , 7
7
csc t = -
Find csc t.
7
7 6
=12
2 6
1
A point on the terminal side of an angle
1 1
Find cos .
7) (- , )
2 5
is given. Find the exact value of the indicated trigonometric function of .
-
1
2
1 2
1 2
r2 = +
2
5
cos
=
r=
1
1
+
4 25
cos
=-
r=
25 + 4
100
cos
=-
5
29
cos
=-
5 29
29
r=
29
10
29
10
1
10
·
2
29
Find the exact value.
8) sec 30°
sec 30° =
sec 30° =
1
1
2
=
=
cos 30°
3
3
2
2 3
3
Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a
calculator.
9) sin 855°
sin 855° = sin 135° + 720° = sin 135°=
sin 855° =
2
2
2
2
10) cos
14
3
cos
14
3
= cos
cos
14
3
=-
2
12
+
3
3
= cos
2
1
=3
2
1
2
BONUS. Solve the problem. (6 points)
11) A pendulum swings though an angle of 25° each second. If the pendulum is 40 inches long, how far does its tip
move each second? If necessary, round the answer to two decimal places.
2