Math 8
EXAM 2
FALL 2009
Solve the problem.
1) The minute hand of a clock is 5 inches long. How far does the tip of the minute hand move in 55 minutes? If
necessary, round the answer to two decimal places.
s=5
55
60
28.78
or 28.80
2) As part of an experiment to test different liquid fertilizers, a sprinkler has to be set to cover an area of 140
square yards in the shape of a sector of a circle of radius 50 yards. Through what angle should the sprinkler be
set to rotate? Write the answer in degrees minutes seconds, round to the nearest tenth, if necessary.
140 =
1
50 2
2
280 = 2500
280
=
2500
=
280 180°
·
2500
6.417°
6° + .417° ·
60
1°
6°25.03
6°25
6°25 + .03 ·
60
1
6°25 1.7
3) A car is traveling at 38 mph. If its tires have a diameter of 25 inches, how fast are the car's tires turning? Express
the answer in revolutions per minute. If necessary, round to two decimal places. 5280ft = 1 mile
38m 5280ft
1 hr
12 in 1 rev
·
·
·
·
1 hr
1 mi
60 min 1 ft
25
511.18 rpm
or 510.93 rpm
*The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function.
5
39
,Find sec t.
4)
8
8
sec (t) =
8
5
Solve the problem.
5) What is the domain and range of the cosecant function?
D: x | x
n, n is an integer
R:
y| y
- 1 or y
1
1
The point P on the circle that is also on the terminal side of an angle
trigonometric function.
in standard position is given. Find the indicated
6) (-2 6, -15) Find csc .
-2 6 2 + -15 2 = r2
4 6 + 225 = r
24 + 225 = r
249 = r
csc
=
249
249
=-15
-15
Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a
calculator.
7) csc 2,760°
csc 240° + 360(7)
csc(240°)
1
sin(240°)
1
-
3
2
-
2
3
-
2 3
3
Scale the graph. Graph the function. If it is a reciprocal function, graph the reciprocal function as a dashed line and the
given function as a solid line. Show at least two periods. Use an many accurate points as possible. Find (i) the
amplitude, (ii) the period, and (iii) the phase shift. (10 points each)
1
8) y = -2 tan - x
3
2
9) y = -4 sec (3x +
6
)-2
*Write the equation of a sine function in the form y =asin( x - ), that has the given characteristics.
10) Amplitude: 4
Period: 3
Phase Shift:
y = ± 4sin
3
2
x3
3
= ± 4sin
2
2
x3
9
BONUS. Solve the problem. (10 POINTS)
1
, find the exact value of f(a) + f(a - 2 ) + f(a + 4 ).
11) If f(x) = cos x and f(a) = 12
-
1
1
1
3
1
==12 12 12
12
4
3