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Math 128
Exam 1
Spring 2009
Name__________________
SHOW ALL WORK
1) Draw the angle -2π/3 in standard position.
5
2) Convert 210° degrees to radians.
210° = 210° ⋅
π
180
=
21π 7π
=
18
6
3) You only need to do ONE
a) A water sprinkler sprays water over a distance of 20 feet while rotating through and angle
of 120°. What area of lawn receives water?
b) A neighborhood carnival has a Ferris Wheel whose radius is 30 feet. You measure the
time it take for one revolution to be 60 seconds. What is the linear speed (in feet per
minute) of a person riding the Ferris Wheel in a car 30 feet from the axis.
a)
A=
θ ⋅r
2
2
π ⎞
⎛
2
⎟ ⋅ 20
⎜120° ⋅
180° ⎠
⎝
=
2
⎛ 12π ⎞
⎛ 2π ⎞
⎜
⎟ ⋅ 400 ⎜
⎟ ⋅ 400
18 ⎠
3 ⎠
⎝
⎝
=
=
2
2
=
v = rw
b)
2π
400π
⋅ 200 =
3
3
30
w=
v = rw = 30 ft ⋅
1 rev 2π (rad ) 2π (rad )
⋅
=
1 min
min
rev
π
min
= 188.5 ft / min
= 30π ft / min
3
, where θ is an acute angle measured in degrees,
5
a) What is the exact value of sin (-θ ) ? -3/5
4) Given sin θ =
5
b) What is the exact value of cos θ ?
3
4/5
4
c) What is the exact value of cos (90° - θ)?
5)
3/5
Give the exact values of cosθ for the following angles .
π/2
π/6
3
2
0
5π/6
− 3
2
11π/6
3
2
13π/6
3
2
6) The point (2, -3) is on the terminal side of an angle θ. Find the exact value of each of the six
trigonometric functions of θ.
sin θ =
2
-3
cos θ =
−3
13
2
13
−3
tan θ =
2
=
− 3 13
13
=
2 13
13
− 13
3
13
sec θ =
2
−2
cot θ =
3
csc θ =
7) Name the quadrant in which θ lies if sinθ < 0 and tanθ > 0.
III (3rd quadrant)
8) If sin θ = -5/13 and tan θ > 0. Find the exact value of cos θ.
x2 + 25 = 169
x2 = 144
x = ± 12
-5
θ
13
Quadrant III
x = -12
cos θ =
− 12
13
9) A radio transmission tower is 100 feet high. How long should a guy wire be if it is to be
attached to the tower 10 feet from the top and is to make an angel of 65° with the ground?
10
sin 65° =
x=
90
90
x
90
= 99.3 feet
sin 65°
65°
10) What is the period of the tangent function?
π
11) Graph y = -3cos(2x + π/2) (Note when hand drawn the curve should “end” with arrows)
The blue curve is before the shift. Amp -3, period 2π/2 = π.
The final black curve includes a shift of π/4 left since y = -3cos 2(x + π/4)
y = -3cos(2x); -4.000000 <= x <= 4.000000 y
y = -3cos(2x + pi/2); -4.000000 <= x <= 4.000000
3
2
1
x
−π
−3π/4
−π/2
−π/4
π/4
−1
−2
−3
4
π/2
3π/4
π
5π/4
12) Graph y = 2sec(x)
(Again hand drawn curves should have arrows at the end.)
y
4
3
2
1
x
−3π/2
−π
−π/2
π/2
−1
−2
−3
−4
π
3π/2