Question

[Trigonometric Graphs]

Use the following information to write an equation of the graph described:

7. sin; Amp = 2, per = π, vertical shift = down 3.

8. cos; Amp = 1; per = π/4, phase shift = left π.

Explain.​

Answer 1

Answer: 7. y = 2 sin (2x) - 3

`\bold{8.\quad y=sin\bigg(8x + (8)/(\pi)\bigg)}`

Explanation:

The general form of a sine equation is: y = A sin (Bx - C) + D where

• Amplitude = |A|
• Period (P) =
  `(2\pi)/(B)`
• Phase Shift =
  `(C)/(B)`
• Vertical Shift = D (positive is up, negative is down)

7. Given:

• A = 2
• P = π =
  `(2\pi)/(B)` → B = 2
• C = 0 (none)
• D = -3

--> y = 2 sin (2x) - 3

8. Given:

• A = 1
• P =
  `(\pi)/(4)` =
  `(2\pi)/(B)` → B = 8

• 
  `\text{Phase Shift = }-\pi = (C)/(8)\implies C = -8\pi`
• D = 0 (none)

`\implies y=sin\bigg(8x + (8)/(\pi)\bigg)`