Question

A sine curve with a period of 8, an amplitude of 2, a left phase shift of /3, and a vertical translation down 5 units.

Answer 1

Answer:

$y=2sin[\frac{\pi}{4}(x+3) ]-5$

Step-by-step explanation:

The standard form for a sinusoidal function is given by:

y = Asin[B(x - C)] + D

Where A is the amplitude of the sine wave, the period is 2π/B, C is the phase shift and D is the vertical displacement / translation

Given:

A = 2, D = -5 (down), C = -3 (left).

8 = 2π/B; B = π/4

Therefore:

$y=2sin[\frac{\pi}{4}(x+3) ]-5$