A sine curve with a period of 8𝜋, an amplitude of 5, a left phase shift of 𝜋/4, and a vertical translation down 4 units.

Answer 1

Asin(bx -c) + d

where A= amplitutde= 5

b = 2pi/period= 2pi/8pi = 1/4

c = phase shift= pi/4

d = midline = -4

plug in the values

Answer 2

is a sine curve with

1. an amplitude of
2. a period of
3. a right phase shift of
4. a vertical translation up units

To have

1. an amplitude of 5, we need = 5
2. a period of 8π, we need = 2π/8π = 1/4
3. a left phase shift of π/4, we need = –b × π/4 = –1/4 × π/4 = –π/16
4. a vertical translation down 4 units, we need = –4

Answer