Chapter Review
Chapter
Chapter 6
Section
Chapter Review
Purchase this Material for $10
You need to sign up or log in to purchase.
Subscribe for All Access
You need to sign up or log in to purchase.
Solutions 31 Videos

An arc 33 m long subtends a central angle of a circle with a radius of 16 m. Determine the measure of the central angle in radians.

Buy to View
Q1

A circle has a radius of 75 cm and a central angle of \frac{14\pi}{15}. Determine the arc length.

Buy to View
Q2

Convert each of the following to exact radian measure and then evaluate to one decimal.

20°

Buy to View
Q3a

Convert each of the following to exact radian measure and then evaluate to one decimal.

-50°

Buy to View
Q3b

Convert each of the following to exact radian measure and then evaluate to one decimal.

160°

Buy to View
Q3c

Convert each of the following to exact radian measure and then evaluate to one decimal.

420

Buy to View
Q3d

Convert the following to degree measure.

\displaystyle \frac{\pi}{4}

Buy to View
Q4a

Convert the following to degree measure.

\displaystyle -\frac{5\pi}{4}

Buy to View
Q4b

Convert the following to degree measure.

\displaystyle \frac{8\pi}{3}

Buy to View
Q4c

Convert the following to degree measure.

\displaystyle -\frac{2\pi}{3}

Buy to View
Q4d

For each of the following values of \sin \theta, determine the measure of \theta if \frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2}.

\displaystyle \frac{1}{2}

Buy to View
Q5a

For each of the following values of \sin \theta, determine the measure of \theta if \frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2}.

\displaystyle -\frac{5\pi}{4}

Buy to View
Q5b

For each of the following values of \sin \theta, determine the measure of \theta if \frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2}.

\displaystyle \frac{8\pi}{3}

Buy to View
Q5c

For each of the following values of \sin \theta, determine the measure of \theta if \frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2}.

\displaystyle -\frac{2\pi}{3}

Buy to View
Q5d

If \cos \theta = - \frac{5}{13}, and 0 \leq \theta \leq 2\pi, determine

a) \tan \theta

b) \sec \theta

c) the possible values of \theta to the nearest tenth

Buy to View
Q6

A tower that is 65 m high makes an obtuse angle with the ground. The vertical distance from the top of the tower to the ground is 59 m. What obtuse angle does the tower make with the ground, to the nearest hundredth of a radian?

Buy to View
Q7

State the period of the graph of each function, in radians.

(a) y = \sin x

(b) y = \cos x

(c) y = \tan x

Buy to View
Q8

The following graph is a sine curve. Determine the equation of the graph.

Buy to View
Q9

The following graph is a sine curve. Determine the equation of the graph.

Buy to View
Q10

State the transformations that have been applied to f(x) = \cos x to obtain each of the following functions.

\displaystyle f(x) = -19\cos x - 9

Buy to View
Q11a

State the transformations that have been applied to f(x) = \cos x to obtain each of the following functions.

\displaystyle f(x) = \cos(10(x + \frac{\pi}{12}))

Buy to View
Q11b

State the transformations that have been applied to f(x) = \cos x to obtain each of the following functions.

\displaystyle f(x) = \frac{10}{11}\cos(x - \frac{\pi}{9}) + 3

Buy to View
Q11c

State the transformations that have been applied to f(x) = \cos x to obtain each of the following functions.

\displaystyle f(x)= -\cos(-x + \pi)

Buy to View
Q11d

The current, I, in amperes, of an electric circuit is given by the function I(t)= 4.5 \sin (120pt), where t is the time in seconds.

a) Draw a graph that shows one cycle.

b) What is the singular period?

c) At what value of t is the current a maximum in the first cycle?

d) When is the current a minimum in the first cycle?

Buy to View
Q12

State the period of the graph of each function, in radians.

(a) y=\csc x

(b) y = \sec x

(c) y = \cot x

Buy to View
Q13

A bumblebee is flying in a circular motion within a vertical plane, at a constant speed.

The height of the bumblebee above the ground, as a function of time, can be modelled by a sinusoidal function.

At t = 0, the bumblebee is at its lowest point above the ground.

a) What does the amplitude of the sinusoidal function represent in this situation?

b) What does the period of the sinusoidal function represent in this situation?

c) What does the equation of the axis of the sinusoidal function represent in this situation?

d) If a reflection in the horizontal axis was applied to the sinusoidal function, was the sine function or the cosine function used?

Buy to View
Q14

The population of a ski-resort town, as a function of the number of months into the year, can be described by a cosine function. The maximum population of the town is about 15 000 people, and the minimum population is about 500 people. At the beginning of the year, the population is at its greatest. After six months, the population reaches its lowest number of people. What is the equation of the cosine function that describes the population of this town?

Buy to View
Q15

A weight is bobbing up and down on a spring attached to a ceiling. The data in the following table give the height of the weight above the floor as it bobs. Determine the sine function that models this situation.

\displaystyle \begin{array}{llllllll} &t(s) &0.0 & 0.2 & 0.4 & 0.6& 0.8 & 1.0 & 1.2& 1.4 & 1.6 & 1.8 & 2.0 & 2.2 \\ &h(t) &120 & 136 & 165 & 180& 166 & 133 & 120& 135 & 164 & 179 & 165 &133 \end{array}

Buy to View
Q16

State two intervals in which the function

\displaystyle y = 7 \sin(\frac{1}{5}x) + 2 has na average rate of change that is

a) zero

b) a negative value

c) a positive value

Buy to View
Q17

State two points where the function

\displaystyle y = \frac{1}{4}\cos(4\pi x) -3 has an instantaneous rate of change is

a) zero

b )z negative value

c) a positive value.

Buy to View
Q18

A person’s blood pressure, P(t), in millimetres of mercury (mm Hg), is modelled by the function \displaystyle P(t) = 100 -20\cos(\frac{8\pi}{3}t)

a) What is the period of the function?

b) What does the value of the period mean in this situation?

c) Calculate the average rate of change in a person's blood pressure on the interval t \in [0.2, 0.3].

d) Estimate the instantaneous rate of change in a person's blood pressure at t = 0.5

Buy to View
Q19