What is the period, amplitude and phase shift for:
y=2sin(3x-pi)
In
y = a sin k(x - ß)
the amplitude is a
the period is 2pi/k or 360º/k
there is a phase shift of ß to the right.
Yours:
y=2sin(3x-pi)
= 2sin 3(x - pi/3)
so .....
its pi/3 units to the right :)
Yes, that's correct! The amplitude is 2 and the period is 2pi/3.
Why did the sinusoidal function go to the circus? Because it wanted to find its period, amplitude, and phase shift!
Now let me provide you with the information:
Period: The period of a sine function is determined by the coefficient of x. In this case, the coefficient is 3, so the period is 2π/3. This means the sinusoid completes one full cycle every (2π/3) units.
Amplitude: The amplitude of a sine function is the maximum absolute value it reaches. In this case, the amplitude is 2, so the graph will go up and down by a maximum of 2 units.
Phase Shift: The phase shift is determined by the additional term inside the parentheses, in this case, -π. The phase shift occurs horizontally, and in this case, the graph has shifted π units to the right.
So, the period is 2π/3, the amplitude is 2, and the phase shift is π to the right. I hope this information brings a smile to your face!
To find the period, amplitude, and phase shift of the given function y = 2sin(3x - π), we can utilize the general form of a sinusoidal function:
y = A * sin(B(x - C)) + D,
where A represents the amplitude, B determines the frequency and period, C indicates the phase shift, and D represents a vertical shift.
In this case, we have the equation y = 2sin(3x - π).
Amplitude:
The amplitude is the coefficient A. In this equation, A = 2. Therefore, the amplitude is 2.
Period:
The period of a sinusoidal function can be calculated using the formula T = (2π) / |B|, where B corresponds to the coefficient in front of x. In our equation, B = 3. Hence, the period is T = (2π) / |3| = 2π/3.
Phase Shift:
To determine the phase shift, we need to isolate the argument of the sine function, B(x - C), and equate it to 0. In this equation, B = 3, so we have 3x - π = 0.
Now, we can solve for x to find the phase shift:
3x = π,
x = π/3.
Therefore, the phase shift is C = π/3.
In summary, for the given function y = 2sin(3x - π), the amplitude is 2, the period is 2π/3, and the phase shift is π/3.