Name: ___________________
Date: Nov 28, 2018
UNIT # 5 TEST: MHF4U0
Trigonometric Functions
***Communication level is based on clarity of your
solutions, “therefore statements” and use of units.
KNOWLEDGE (24 Marks)
Multiple Choice: Write the letter corresponding to the most appropriate answer for each
question:
1. Which of the following functions has the longest period?
a)
c)
b)
d)
2. For which of the following values of x, is
a)
not defined
b) -
c) 0
3. In which quadrant is the following true?
and
a)
1
b)
2
4. Which function has a point closest to the origin?
a)
c)
b)
d)
5. If
a)
, such that
-1.3181
, then
b)
c)
4.458
b.
c.
9. The graph of
a)
b)
d)
1.3181
.
[-2,2]
[-3,1]
[-3,1]
c) y = cot x
intersects the graph of
4
, the amplitude, period and range are:
Range
y∈R
3
b)
to
d)
d)
d.
2
8. Which of the following functions do not have a y-intercept:
a)
6.0281
from
Period
π
2
π
3
c)
6. Determine the average rate of change of the function
a) 0
b) 1
c)
7. For a trigonometric function,
Amplitude
a.
2
d)
d) both (a) and (c)
at
c)
d)
10. Determine the instantaneous rate of change of the graph 𝑜𝑓 𝑦 = 𝑠𝑖𝑛𝑥 𝑤ℎ𝑒𝑛 𝑥 =
a. 0
b. –1
c. 1
d. undefined
π
2
Full Solution Questions:
11. Given the function
a) Complete the following table:
(K6)
d) Max:
a) The period of the function:
e)Min
f) The domain of the function is:
b) The phase shift of the function:
g) Range:
c) amplitude:
b) Graph 2 cycles of the above function:
(K4)
12. Use an algebraic method to solve the following equations. Show all your work for full marks.
a.
, where
.
APPLICATION (27 marks)
13. Use an algebraic method to solve the following equations. Show all your work for full marks.
2
6𝑐𝑜𝑠 𝑥 + 𝑐𝑜𝑠𝑥 − 1 = 0 , where
c. 𝑐𝑜𝑠𝑥 +
2
2
= 0 on the interval
.
14. A Ferris wheel is 40 cm in diameter and the base is 5 cm off the ground. It can make one rotation in
5 min. and people get on the ride from the lowest point (base).
a) Graph a sketch (rough) which models the above relationship between height (cm) and time(s)
b) Determine a Sinusoidal equation, which models the height (cm) of the Ferris wheel as the time
changes in seconds.
c) Determine the time(s) when the height of the Ferris wheel is 30 cm or higher.
15. Determine the Sine & Cosine equation of the following graph of a function.
Sine equation: _________________________
Cosine equation: _________________________
15. A pebble is embedded in the tread of a rotating bicycle wheel of diameter 80 cm. The wheel rotates at
4 revolutions per second.
a) Determine a relationship between the height, h, of the pebble above the ground, in centimetres, as a
function of time t, in seconds.
b) Use the equation from you answer in part a) to calculate the instantaneous rate of change of the
pebble at 1.3 seconds. Round your answer to two decimal places.