Question

For a short time after a wave is created by wind, the height of the wave can be modeled using y = a sin , where a is the amplitude and T is the period of the wave in seconds.

13. Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.
amplitude: 4, period 4 phase shift = vertical shift = -2

Answer 1

`\bold{\text{Answer:}\quad y=4\ sin\bigg((\pi)/(2)x\bigg)-2}`

Explanation:

y = A sin (Bx - C) + D

• A: Amplitude
• Period = 2π/B
• Phase Shift = C/B
• D: Vertical shift

Given: A = 4, Period = 4, Phase Shift = none (0), D = -2

`\text{Period}=(2\pi)/(B)=4\quad \rightarrow \quad B=(\pi)/(2)`

`\large\boxed{y=4\ sin\bigg((\pi)/(2)x\bigg)-2}`