Question

[Trigonometric Graphs]

Answer 1

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

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

Step-by-step explanation:

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

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

7. Given:

• A = 2
• P = π = $\dfrac{2\pi}{B}$  → B = 2
• C = 0 (none)
• D = -3

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

8. Given:

• A = 1
• P = $\dfrac{\pi}{4}$ = $\dfrac{2\pi}{B}$  → B = 8

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

$\implies y=sin\bigg(8x + \dfrac{8}{\pi}\bigg)$