Write an equation in terms of x and y for

Tahmid Knox 2021-08-18 Answered

Write an equation in terms of x and y for the function that is described by the given characteristics. A sine curve with a period of π, an amplitude of 3, a right phase shift of π2, and a vertical translation up 2 units.

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Expert Answer

Jozlyn
Answered 2021-08-19 Author has 85 answers

The graph of y=asinb(xd)+c or y=acosb(xd)+c, has: amplitude ∣a∣, period 2πb, vertical tration c units up if c>0 or c units down if c<0, and phase shift dd units to the right if d>0 or ∣d∣ units to the left if d<0.

Use the sine function:

y=asinb(xd)+c

The period is π so P2πb=π2. The amplitude is 3 so a=∣3∣=3

The phase shift is π2 right so d=π2. The vertical traation is 2 units so d=2. So, the equation is:

y=3sin2(xπ2)+2

or y=3sin(2xπ)+2

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