Give the following for the function: y=2+cos(5x+3.14
Amplitude:
Period:
Phase Shift:
amplitude = 1
period is when 5 x = 2 pi
so when x = (2/5) pi
phase shift is 3.14 radians or about pi
I must respectfully disagree with Damon's answer for the phase shift
changing it to
y = 2 + cos 5(x + 3.14/5)
we can see that the phase shift is 3.14/5 to the left
or π/5 to the left
To find the amplitude, period, and phase shift of the function y = 2 + cos(5x + 3.14), we can use the standard form of a cosine function: y = A*cos(B(x - C)) + D.
The general form of a cosine function is: y = a*cos(b(x - c)) + d, where a represents the amplitude, b represents the frequency, c represents the phase shift, and d represents the vertical shift.
In our given function y = 2 + cos(5x + 3.14), we can see that:
- There is no coefficient in front of the cosine function, so the amplitude is 1 (by default).
- The coefficient in front of x is 5, which represents the frequency. The frequency is calculated as f = 2π/B, so B = 5, and the period is 2π/5.
- The phase shift is determined by the term inside the cosine function, which is 5x + 3.14. To find the phase shift, solve for x when 5x + 3.14 = 0: 5x = -3.14, x = -3.14/5. Therefore, the phase shift is -3.14/5.
To summarize:
Amplitude: 1 (default)
Period: 2π/5
Phase shift: -3.14/5
Note: The vertical shift, represented by the term 2 in the given function, is not needed to find the amplitude, period, and phase shift, as it only affects the vertical position of the graph.