Trig Functions Chapter Test, pg346
Chapter
Chapter 5
Section
Trig Functions Chapter Test, pg346
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Solutions 15 Videos

The period of the function is?

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Q1

The amplitude of the function is?

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Q2

The value of f(12) is

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Q3

For \displaystyle y = \frac{3}{8}\cos[5(x - 30^o)] + \frac{3}{4}

the period of the function is

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Q4

For \displaystyle y = \frac{3}{8}\cos[5(x - 30^o)] + \frac{3}{4}

the minimum value of the function is

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Q5

For \displaystyle y = \frac{3}{8}\cos[5(x - 30^o)] + \frac{3}{4}

with respect to y = \cos x, the phase shift of the function is

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0.00mins
Q6

For \displaystyle y = \frac{3}{8}\cos[5(x - 30^o)] + \frac{3}{4}

with respect to y = \cos x, the phase shift of the function is

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Q7

Consider the function y = 2 \cos (3x + 120^o). What is the phase shift of the function?

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Q8

Consider the function y = 3\sin[4(x + 60^o)]

a) What is the amplitude of the function?

b) What is the period of the function?

c) Describe the phase shift of the function.

d) Describe the vertical shift of the function.

e) Graph the function one step at a time. Label each step according to the transformation taking place.

f) State the domain and range of the transformed function. Use set notation.

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Q9

A sinusoidal function has an amplitude of 4 units, a period of 90°, and a maximum at (0, 2).

a) Represent the function with an equation using a cosine function.

b) Represent the function with an equation using a sine function.

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Q10

A sinusoidal function has an amplitude of \frac{1}{4} units, a period of 720°, and a maximum point at (0, \frac{3}{4}).

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Q11

Consider the function \displaystyle y = 2\cos[3(x - 120^o)] .

a) Determine the amplitude, period, phase shift, and vertical shift with respect to y= \cos x.

b) What are the maximum and minimum values?

c) Find the first three X-intercepts to the right of the origin.

d) Find the y—intercept.

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Q12

a) Determine the equation of the sine function shown.

b) Suppose that the maximum values on the graph are half as far apart. How does the equation in part a) change? Justify your answer.

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Q13

A summer resort town often shows seasonal variations in the percent of the workforce employed. The table lists the percent employed on the first of each month, starting in January, for 1 year.

a) Construct a model for these data using either a sine function or a cosine function. State the amplitude, period, phase shift, and vertical shift.

b) Graph the model on the same set of axes as the data. Comment on the fit.

c) Use your model to predict the employment level on June 15.

d) Economic forecasters predict a mild recession for the following year that will decrease employment levels for each month by 10%. Describe the effect that this will have on the graph of the function.

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Q14

The Ferris wheel at a carnival has a diameter of 18 m and descends to 2 m above the ground at its lowest point. Assume that a rider enters a car at this point and rides the wheel for two revolutions.

a) Model the rider’s height above the ground versus the angle of rotation using a transformed sine function.

b) Suppose that the rider enters the car from a platform located 45° along the rim of the wheel before the car reaches its lowest point. Adjust your model in part a) to reflect this situation.

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Q15