Course: 112 Precalculus Part 2
Instructor: R. Porter
Sample Exam 2
( Please note that Prof. Porter Likes to use the graphing calculator and this exam may reflect this fact. Other professors may choose more traditional methods.)
(to two decimal places)
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b) What is the reference number when t = 2?
(to two decimal places)
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c) Find the terminal point P(x,y) on the unit circle determined by t = -5p /6
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d) Find the reference number
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2) a) Change -150 degrees to radians.
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b) Determine the exact value of the trig function at the given real number. sec (-150o)
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3) Given that sin x = 3/4 and tan x < 0, find remaining trig values:
cos x = _____________
tan x = _____________
sec x = _____________
csc x = _____________
cot x = _____________
4) Graph one period of the function f(x) = 3 sin (x/8 - p /8)
5) Find the period, amplitude, phase shift for the function in 4.
Period:__________________
Amplitude:_______________
Phase Shift:______________
6) a) Given the data, find an exponential regression.
|
Time |
20 |
25 |
30 |
|
Height |
100 |
110 |
150 |
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b) If a regression of y = a * b ^ x ( with a = 42.9 and b = 1.04 corretation = .91 ) is found, use the data to predict the height at 24 seconds.
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c) Is your regression good ? Why?
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7) Given the data, come up with an appropriate model y = A sin ( B x + C) + D
|
Year |
1979 |
1980 |
1981 |
1982 |
1983 |
1984 |
1985 |
|
Profits |
55 |
25 |
55 |
85 |
55 |
25 |
55 |
A = ____ B = ____ C = _____ D = _____
8) Graph one period of the function f(x) = 6 tan (3x - p /3)
9) Give the period and phase shift for the function in 8)
Period:__________________
Phase Shift:______________
10) Find the length of an arc that subtends a central angle of 30 degrees in a circle of radius 15.
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|
Year |
1979 |
1980 |
1981 |
1982 |
1983 |
1984 |
1985 |
|
Profits |
3 |
4 |
3 |
2 |
3 |
4 |
3 |
b) What type of regression would you use to model the situation.
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c) Predict the profits in 1995.
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12) Fifteen miles away from the peak of a mountain top an observer notes that the angle of elevation to the top of the mountain is 12 degrees. How high is the mountain?
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13) a) Find the terminal point on the unit circle when x = 2/3 and in Quadrant 1?
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b) What is the angle corresponding to the terminal point above in degrees?
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14) An airplane travelling at a speed 400 miles per hour and an altitude of 2 miles begins to descend at an angle of 8 degrees. How long will the plane take to land?
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