Multiple Choice
Identify the
choice that best completes the statement or answers the question.
|
|
|
1.
|
  radians is equal to how many degrees?
|
|
|
2.
|
The exact radian measure for an angle of 255° is
|
|
|
3.
|
Determine the equation of a circle with centre at the origin and radius
8.
|
|
|
4.
|
Determine the equation of a circle with centre at (3, –3) and radius
10.
|
|
|
5.
|
Determine the measure of the angle in standard position shown on the graph
below. Round your answer to the nearest tenth of a degree. A. | 161.6° | C. | 71.6° | B. | 341.6° | D. | 251.6° |
|
|
|
6.
|
Which is a possible value of q, to the nearest
hundredth of a radian, when cos q =
–0.58?
A. | –2.19 | C. | 2.19 | B. | –0.62 | D. | 0.84 |
|
|
|
7.
|
A tricycle has a front wheel that is 30 cm in diameter and two rear wheels that
are each 12 cm in diameter. If the front wheel rotates through a angle of 32°, through how many
degrees does each rear wheel rotate, to the nearest tenth of a degree?
A. | 32.0° | C. | 80.0Á | B. | 40.0Á | D. | 160.0Á |
|
|
|
8.
|
Determine the point in quadrant II where the line represented by  intersects the
unit circle. A. | (0.95, –0.32) | C. | (–0.35, 0.94) | B. | (–0.32, 0.95) | D. | (–0.32,
0.94) |
|
|
|
9.
|
Which function, where x is in radians, is represented by the graph shown
below? 
|
|
|
10.
|
The period (in degrees) of the graph of  is
|
|
|
11.
|
Which graph represents the function y =  cos(  x),
where x is in degrees?
|
|
|
12.
|
Which function is represented by the graph shown below, where x is in
degrees? A. | y = sin( x) | C. | y = cos( x) | B. | y =
cos(x) | D. | y
= sin(x) |
|
|
|
13.
|
What is the period of the sinusoidal function  ?
|
|
|
14.
|
Which graph represents the sinusoidal function  ?
|
|
|
15.
|
Given the trigonometric function  , which is the x-coordinate at
which the function is undefined?
|
|
|
Use the following information to answer the questions.The height,
h, in centimetres, of a piston moving up and down in an engine cylinder can be modelled by the
function  , where t is the time, in seconds.
|
|
|
16.
|
What is the piston’s minimum height?
A. | 14 cm | C. | 0 cm | B. | –14 cm | D. | 7 cm |
|
|
|
17.
|
Simplify  . Round your answer to the nearest hundredth. A. | 0.47 | C. | –0.75 | B. | –1.15 | D. | 0.42 |
|
|
|
18.
|
Simplify  .
|
|
|
19.
|
 is equivalent to
|
|
|
20.
|
What is the general solution, in radians, to the equation  ? A. |  where  | C. |  where  | B. | no solution | D. |  where  |
|
Short Answer
|
|
|
1.
|
Find the exact value of  .
|
|
|
2.
|
Sketch the graph of  for two cycles and state the domain, range, period, and
equations of the asymptotes. x is measured in radians.
|
|
|
3.
|
Use a counterexample to show that  is not an identity.
|
|
|
4.
|
Prove the identity  .
|
|
|
5.
|
Is the equation  true for all values of q?
|
Problem
|
|
|
1.
|
The point (–5, 7) is located on the terminal arm of ÐA in standard position.
a) Determine the primary trigonometric
ratios for ÐA.
b) Determine the primary trigonometric
ratios for ÐB with the same sine as ÐA, but different signs for the other two primary trigonometric
ratios.
c) Use a calculator to determine the measures of ÐA and ÐB, to the nearest degree.
|
|
|
2.
|
The table shows the fraction of the Moon that can be seen at midnight from
Simone’s town. Day 1 represents January 1. Day | 1 | 2 | 3 | 4 | 5 | 6 | 10 | 14 | 19 | 21 | Fraction
Visible | 0.25 | 0.17 | 0.12 | 0.06 | 0.02 | 0.00 | 0.10 | 0.56 | 0.98 | 1.00 | | | | | | | | | | | |
| Day | 24 | 30 | 35 | 41 | 45 | 51 | 56 | 60 | 65 | 66 | Fraction
Visible | 0.78 | 0.33 | 0.02 | 0.15 | 0.65 | 1.00 | 0.78 | 0.30 | 0.01 | 0.00 | | | | | | | | | | | |
a) What is the period of the sine function that could be used to
model the data? b) What is the amplitude of the function? c) What is the phase
shift of the function? d) What is the vertical shift? e) Use your answers to
parts a) to d) to write an equation for the function. f) Use your function to determine the
fraction of the moon visible to Simone on day i) 100 ii) 150 iii)
200
|
|
|
3.
|
Simon is due north of a tall totem pole and walks 75 m, 40° west of south.
From his new position, the totem pole is due east, with an angle of elevation of 17°. Determine
the height of the totem pole, to the nearest tenth of a metre.
|