Download Practice Questions answerkey

Practice Questions
1. If s denotes the length of the arc of a circle of radius r subtended by
a central angle θ, find the missing quantity:
a. r = 6.22 centimeters, θ = 1.8 radians, s = 11.2cm
b. r= 23 feet, s=14 feet, θ = 0.609 radians
2. The minute hand of a clock is 7 inches long. How far does the tip of
the minute hand move in 5 minutes? If necessary, round the
answer to two decimal places. 3.67 in
3. An irrigation sprinkler in a field of lettuce sprays water over a
distance of 30 feet as it rotates through an angle of 120°. What
area of the field receives water? If necessary, round the answer to
two decimal places. 942.48 ft2
4. A pick-up truck is fitted with new tires which have a diameter of
40 inches. How fast will the pick-up truck be moving when the
wheels are rotating at 445 revolutions per minute? Express the
answer in miles per hour rounded to the nearest whole number.
53 mph
For 5 and 6 : two sides of a right triangle ABC (C is the right
angle) are given. Find the indicated trigonometric function
of the given angle.
5. Find csc B when a = 7 and b = 2.
√
6. Find cot A when a = 6 and c = 7.
√
√
7. If sinθ=
, cosθ= then find all the other trig functions. (Use
fundamental identities.)
√
tanθ= , cotθ=
8. Find the value of
√
, cscθ=
√
, secθ=
. Do not use a calculator. -1
9. A barge is located 200 feet away from the coastline 1200 feet down
the coast from a power source at point A. To supply the barge with
electricity, a power line will be run from point A to a point B on the
coast and then from point B to the barge. If power lines on land
coast $3 per foot and power lines under water cost $5 per foot,
calculate the total cost of running a power line from point A to the
barge when point B is 800 feet down the coast from point A in the
direction of the barge. Recalculate the total cost when the distance
from A to B is increased in 50-foot increments, until you locate a
possible minimum cost. Interpret your solution.
$4636.07; The minimum cost is $4400 when the point is chosen 1050 feet to
the right of A.
Part I: calculate the total cost of running a power line from point A to the barge
Let distance (A to B) = L and distance (B to barge) = W
Cost function = 3*L + 5*W = 2400 + 5*W (since L = 800)
We can express W =√
=447.2136
Cost =3*800 + 5*447.2136 =4636.07
Part II: Recalculate the total cost when the distance from A to B is increased in 50-foot
increments, until you locate a possible minimum cost
C
θ
Let’s rewrite our Cost function = 3*(800 + P) + 5Q = 2400 + 3P + 5Q
Where P is the amt you increase the power lines on land (in addition to 800 ft)
And Q is the length of the power line in water.
To achieve the minimum value you need to increase θ such that the cost function is
minimized.
The distance A to B is 800 and B to C is 400.
Using right angle trig I can express Q and P as
Q=
, P = 400Cost Function = 2400 +3*(400 = 3600 -
+
)+ 5*
Plotting in excel we our cost function looks as below:
Radians
Cost function
4650
4600
Cost function
0.46
4636.07
0.50
4587.54
0.60
4494.01
0.70
4439.93
4550
0.80
4411.28
4500
0.90
4400.48
4450
1.00
4403.14
4400
1.10
4416.69
1.20
4439.65
1.30
4471.25
1.40
4511.28
4350
0
0.5
1
1.5
2
1.50
4559.96
1.60
4617.95
1.57
4600.00
10. A building 260 feet tall casts a 70 foot long shadow. If a person
looks down from the top of the building, what is the measure of the
angle between the end of the shadow and the vertical side of the
building (to the nearest degree)? (Assume the personʹs eyes are
level with the top of the building.)
15°
11. The point (
√
) on the unit circle corresponds to a real number t
is given. Find all six trig functions.
√
√
sinθ=
tanθ=
, cotθ=
√
, cscθ=
12. Use a coterminal angle to find
√
a. cos 765°
b. csc
√
13. Name the quadrant in which the angle θ lies:
a. tan θ > 0, sin θ < 0 - Quadrant III
b. csc θ > 0, sec θ > 0 - Quadrant I
√
, secθ=
Find the reference angle of the given angle and all six trig
functions for each of the following:
a. 100 ° 80° (use calculator to find trig funcs)
b. -391 ° 31° (use calculator to find trig funcs)
c.
(using unit circle, sin =√ , cos = , tan = ,
14.
√
csc = , sec =√ , tan = )
√
A study of ice cream consumption over 30 four-week periods in
the early 1950s gives rise to the equation C = 0.3520 + 0.0786
sin(0.4806θ - 0.1691) where θ is the number (from 1 to 30) of the
four-week period and C is the ice cream consumption in pints per
capita. Determine the consumption for the tenth four-week period.
Round answer to the nearest 0.001 pint. 0.274 pint
15.
16.
If f(θ) = tan θ and f(a) = -3, find the exact value of f(-a). 3
17. Find the exact value of the expression. Do not use a calculator.
a. sin (2π) + cos (
b. csc ( ) sec (
18.
)=0
) =2
Use transformations to graph the following functions:
a. y = 3 sin x + 5
b. y = cos (x - π)
c. y = -tan(
)
d. y = cot(
e. y = csc(
)
)
19. What is the y-intercept of :
a. y = tan x? 0
b. y = csc x? not defined
20. The data below represent the average monthly cost of natural gas
in an Oregon home.
26) The data below represent the average monthly cost of natural gas in an Oregon home.
M onth
Cost
A ug
21.20
Sep
28.24
M onth Feb
Cost
111.30
M ar
106.26
Oct
44.73
A pr
89.77
N ov
67.25
M ay
67.25
Dec
89.77
Jun
43.73
Jan
106.26
Jul
28.24
Above is the graph of 45.05 sin x superimposed over a scatter
diagram of the data. Find the sinusoidal function of the form y = A sin
(ωx - φ) + B which best fits the data.
A bove is the graph of 45.05 sin x superimposed over a scatter diagram of the data. Find the sinusoidal function
of the form y = A sin ( x - ) + B w hich best fits the data.
2
45.05sin[
+ 66.25
A) y = 45.05 ]sin
xB) y = 45.05 sin
t + 12 + 21.20
+ 66.25
6
3
8
C) y = 45.05 sin
4
x-
2
3
+ 21.20
D) y = 45.05 sin
Page 584
6
x-
12
+ 66.25