Answer: 7. y = 2 sin (2x) - 3
[tex]\bold{8.\quad y=sin\bigg(8x + \dfrac{8}{\pi}\bigg)}[/tex]
Step-by-step explanation:
The general form of a sine equation is: y = A sin (Bx - C) + D where
- Amplitude = |A|
- Period (P) = [tex]\dfrac{2\pi}{B}[/tex]
- Phase Shift = [tex]\dfrac{C}{B}[/tex]
- Vertical Shift = D (positive is up, negative is down)
7. Given:
- A = 2
- P = π = [tex]\dfrac{2\pi}{B}[/tex] → B = 2
- C = 0 (none)
- D = -3
--> y = 2 sin (2x) - 3
8. Given:
- A = 1
- P = [tex]\dfrac{\pi}{4}[/tex] = [tex]\dfrac{2\pi}{B}[/tex] → B = 8
- [tex]\text{Phase Shift = }-\pi = \dfrac{C}{8}\implies C = -8\pi[/tex]
- D = 0 (none)
[tex]\implies y=sin\bigg(8x + \dfrac{8}{\pi}\bigg)[/tex]
