PCM 12
Ch 5.4 HW
Name:_____Key________
1. The partial sinusoidal graphs shown below are intersected by the line y = 6. Each point of
intersection corresponds to a value of x where y = 6. For each graph shown determine the
approximate value of x where y = 6.
a) From the graph, x ≈ 1.3 and x ≈ 4.6.
b) From the graph, x ≈ –3, –2, 0.1, 1.1, 3.2, 4.2, 6.3, and 7.3.
2. The partial graph of a sinusoidal function y = 4 cos (2(x – 60°)) + 6 and the line y = 3 are shown below.
From the graph determine the approximate solutions to the equation 4 cos (2(x – 60°)) + 6 = 3.
From the graph, the solutions to the equation 4 cos (2(x – 60°)) + 6 = 3 are
x ≈ –50°, –10°, 130°, 170°, 310°, and 350°.
3. Solve each of the following equations graphically. (Use technology)
In the interval 0 ≤ x ≤ 2π,
the solutions are x = 0 and x = 6.
In the interval 0º ≤ x ≤ 360º,
There are 4 solutions, and they are
x ≈ 4.8°, 85.2°, 184.8°, and 265.2°.
4. Solve each of the following equations. (Use technology)
The general solution is x ≈ 1.91 + πn
and x ≈ 3.09 + πn, where n ϵ I.
The general solution is x ≈ 4.5° + (8°)n
and x ≈ 7.5° + (8°)n, where n ϵ I.
5. Determine the period, the sinusoidal axis, and the amplitude for each of the
following.
a) The first maximum of a sine function occurs at the point (30°, 24), and the first
minimum to the right of the maximum occurs at the point (80°, 6).
Period: 2(80° – 30°) = 100°,
amplitude:
Sinusoidal axis: y = 6 + 9 = 15 (centre line)
b) The first maximum of a cosine function occurs at (0, 4), and the first minimum to
the right of the maximum occurs at (2π/3, –16)
Period: 2(
– 0) =
,
amplitude:
Sinusoidal axis: y = ‒16 + 10 = ‒6 (centre line)
9. A point on an industrial flywheel experiences a motion described by the function
h(t) = 13
where h is the height, in metres, and t is the time, in min.
a) What is the maximum height of the point?
According to graph, the maximum height of the
Point is 15 + 13 = 28 m.
b) After how many minutes is the maximum height reached?
The maximum height is reached at 0 min, 0.7 min, 1.4 min ….
It seems that every 0.7 min, the max. height is reached.
c) What is the minimum height of the point?
The minimum height of the point is 15 – 13 = 2 m.
d) After how many minutes is the minimum height reached?
The minimum height is reached at 0.35 min, 1.05 min, 1.75 min ….
It seems that every 0.7 min, the min. height is reached.
e) For how long, within one cycle, is the point less than 6 m above the ground?
Within one cycle, the point is less than 6 m
above the ground for approximately
0.44 – 0.26 = 0.18 min.
f) Determine the height of the point if the wheel is allowed to turn for 1 h 12 min.
1 h 12 min = 72 min
h (72) = 13
≈ 23.1 m
The height of the point if the wheel is allowed to turn for 1 h 12 min is
approximately 23.1 m.