Chapter Review
Chapter
Chapter 5
Section
Chapter Review
Solutions 15 Videos

Which of the following values do you expect to follow a periodic pattern? Justify your answer for each case

a) the distance from the centre as a grandfather clock pendulum swings back and forth

b) the cost of sending a package by courier. Which varies depending on the weight of the package

c) the value of a stock over a 1-year period

Q1

a) Sketch a periodic function, f(x), with a maximum value of 8, a minimum of -5, and a period of 3.

b) Select a value a for x, and determine f(a).

c) Determine two other values, b and c, such that f(a) = f(b) = f(c).

Q2

Copy and complete the table of values for y = sin 2x.

Q3a

Use the table values to sketch a graph of y = sin 2x. On the same set of axes, sketch a graph of y = sin x

Q3b

Compare the graphs in part b). Describe the similarities and differences.

Q3c

a) Predict what the graph of y = -csc x looks like. Use a table of values or technology to sketch the graph. Is your prediction correct?

b) Sketch the graph of y = csc x on the same set of axes.

c) Describe the similarities and differences between the graphs.

Q4

Write two equations, one in the form y = a sin kx and one in the form y = a cos [k(x - d)], to match the graph.

Q5

Write two equations, one in the form y = a cos kx and one in the form y = a sin[k(x - d)], to match the graph.

Q6

Determine the amplitude, the period, the phase shift, and the vertical shift of each function.

a) y = 5 sin [3(x - 40^{\circ})] + 6

b) y = \dfrac{1}{4} cos [4x + 400^{\circ}] - 2

c) y = -7 sin [\dfrac{2}{3}(x + 75^{\circ})] - 1

d) y = 0.4 cos [3.5(x - 60^{\circ})] + 5.6

Q7

a) Transform the graph of f(x) = sin x to g(x) = -7 sin[\dfrac{1}{2}(x- 30^{\circ})] + 1. Show each step in the transformation.

b) State the domain and range of f(x) and g(x).

Q8

a) Transform the graph of f(x) = cos x to g(x) = \dfrac{2}{3} cos[5(x + 28^{\circ})] - 4. Show each step in the transformation.

b) State the domain and range of f(x) and g(x).

Q9

Determine the equation of a sine function that represents the graph shown.

Q10a

Determine the equation of a cosine function that represents the graph.

Q10b

The table shows the mid-season high temperatures for winter, spring, summer, and fall over a 3-year period for a city in Ontario.

a) Use the table to determine a sinusoidal model for the mid-season high temperature.

b) Graph the points in the table on the same axes as your model to verify the fit.

c) Is the fit as you expect? Explain any discrepancies.

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Q11

During a 12-h period, the tides in one area of the Bay of Fundy cause the water level to rise to 6 m above average sea level and to fall 6 m below average sea level. The depth of the water at low tide is 2 m.

a) Suppose the water is at average sea level at midnight and the tide is coming in. Draw a graph that shows the height of the tide over a 24-h period. Explain how you obtained the graph.

b) Determine an equation that represents the tide for part a) using

i) a sine function

ii) a cosine function

c) Suppose the water is at average sea level at 3 am. and the tide is coming in. Write an equation that represents this new situation. Explain your reasoning.