State the amplitude, period, and phase shift of the function.
h(t)=-9cos(7t-Pie/5)
I got the amplitude and the period. For the phase shift I got (Pie/5)/7 but its wrong. Can someone tell me what I did wrong?
h(t)=-9cos(7t-π/5)
or
h(t)=-9cos 7(t-π/35)
the phase shift is π/35 to the right,
your answer of π/5/7 is actually right, except it is not written in good form. It is ambigious, does it mean
(π/5) / 7 or π/(5/7)
To find the amplitude, period, and phase shift of the function h(t) = -9cos(7t-π/5), let's break down each component:
1. Amplitude: The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine term. In this case, the coefficient is -9, so the amplitude is | -9 | = 9.
2. Period: The period of a cosine function can be calculated by dividing 2π by the coefficient of t inside the cosine term. In this case, the coefficient is 7, so the period is 2π / 7.
3. Phase Shift: The phase shift determines the horizontal shift of the graph. It can be found by equating the argument of the cosine term to zero and solving for t. In this case, we have 7t - π/5 = 0. Solving for t gives us t = π/5 / 7.
It seems like you made a small error while calculating the phase shift. Let me explain the correct steps:
Start with 7t - π/5 = 0
Add π/5 to both sides: 7t = π/5
Divide both sides by 7: t = π/5 / 7
Therefore, the correct phase shift is t = π/5 / 7.
To summarize:
- Amplitude = 9
- Period = 2π/7
- Phase Shift = π/5 / 7
I hope this clears up any confusion and helps you in solving similar problems in the future.