State the amplitude, period, and phase shift of the function.
h(t)=-9cos(7t-Pie/5)
I will be happy to critique your thinking.
amp is 9, period os (2pie)/(pie/5)
and phase shift is (pie/5)/7
To determine the amplitude, period, and phase shift of the function h(t) = -9cos(7t - π/5), we can look at the general form of a cosine function:
y = A*cos(B(x - C))
- Amplitude (A): The amplitude is the absolute value of the coefficient A, which is the number multiplying the cosine function. In this case, A = -9, so the amplitude is 9 (since the amplitude is always positive).
- Period: The period of a cosine function is given by 2π/B, where B is the coefficient multiplying the variable inside the cosine function. In this case, B = 7, so the period is 2π/7.
- Phase Shift: The phase shift represents the horizontal shift or displacement of the graph in the x-direction. It is given by C. In the given function, C = π/5. However, keep in mind that the sign of C is opposite to what is written in the function. So, in this case, there is a phase shift of -π/5 to the right.
Summary:
Amplitude = 9
Period = 2π/7
Phase Shift = -π/5 (to the right)