#1
Which of the following represents the amplitude of a sinusoidal function?
The coefficient of the sine or cosine function
ExplanationAmplitude is determined by the coefficient of sine or cosine.
#2
What does the term 'period' refer to in a sinusoidal function?
The length of one complete cycle of the function
ExplanationPeriod represents the duration of one complete cycle.
#3
What is the angular frequency of a sinusoidal function with a period of 2π?
1
ExplanationAngular frequency is 1 for a period of 2π.
#4
In a sinusoidal function of the form y = A sin(Bx + C), what does 'C' represent?
Phase shift
Explanation'C' represents the phase shift of the function.
#5
What is the vertical shift of the sinusoidal function y = 3 cos(2x) + 4?
4
ExplanationThe vertical shift is 4 units.
#6
In a sinusoidal function of the form y = A sin(Bx - C) + D, what role does 'D' play?
It represents the vertical shift of the function
Explanation'D' indicates the vertical displacement of the function.
#7
For a sinusoidal function, what effect does increasing the value of 'B' have?
It compresses the graph horizontally
ExplanationIncreasing 'B' leads to a horizontal compression of the graph.
#8
For a sinusoidal function, what happens if the amplitude 'A' is negative?
The graph is reflected across the x-axis
ExplanationA negative 'A' reflects the graph across the x-axis.
#9
What is the phase difference between two sinusoidal functions with the same amplitude, period, and frequency, but one being a sine function and the other a cosine function?
π/2
ExplanationThe phase difference is π/2 between sine and cosine functions.
#10
What is the phase shift of the sinusoidal function y = 2 sin(3x - π/2)?
π/2 units to the left
ExplanationThe phase shift is π/2 units to the left.
#11
What is the phase shift of the sinusoidal function y = 2 cos(3x - π/4)?
π/4 units to the right
ExplanationThe phase shift is π/4 units to the right.
#12
In a sinusoidal function of the form y = A sin(Bx - C) + D, what is the range of the function if -1 ≤ sin(Bx - C) ≤ 1?
[D - A, D + A]
ExplanationThe range is [D - A, D + A] when -1 ≤ sin(Bx - C) ≤ 1.
#13
If the period of a sinusoidal function is 2π and the phase shift is π/3, what is the equation of the function in the form y = A sin(Bx - C) + D?
y = sin(2x - π/3)
ExplanationThe equation is y = sin(2x - π/3) given the period and phase shift.
#14
For a sinusoidal function, if the amplitude is 4 and the period is π, what is the equation of the function in the form y = A sin(Bx - C) + D?
y = 4 sin(2x)
ExplanationThe equation is y = 4 sin(2x) given the amplitude and period.