Find period and phase shift and amplitude of
y=10sin(x/4)-4pi)-5?
The amplitude =10
Period=?
Phase shift=?
If you mean
10sin((x/4)-4π)-5
then that is
10sin((x-16π)/4)-5
period = 2π/(1/4) = 8π
shift = 16π
To find the period and phase shift of the given function, let's first look at the general form of a sinusoidal function:
y = A * sin(B(x - C)) + D
In this equation:
- A represents the amplitude
- B determines the period (period = 2π/B)
- C represents the phase shift (horizontal shift)
- D represents the vertical shift
Now, let's break down the given function: y = 10sin(x/4 - 4π) - 5
Comparing this to the general form, we can identify the values:
A = 10 (amplitude)
B = 1/4 (B = 1/period)
C = 4π (phase shift)
D = -5 (vertical shift)
Amplitude: The amplitude is given directly, which is 10.
Period: To find the period, we use the formula period = 2π/B.
In this case, B = 1/4, so the period = 2π / (1/4) = 8π.
Phase Shift: To find the phase shift, we look at the value of C. In this case, C = 4π, so the phase shift is 4π to the right.
Therefore, the period is 8π, and the phase shift is 4π to the right.