Question

How do you determine period, amplitude and phase shift for `y = 3 + 2 csc ( x/2 - pi/3 )`?

Answer 1

As below.

Explanation:

Standard form of the cosecant function is `y = A csc (Bx - C) + D`

Given `y = 2 csc (x/2 - pi/3) + 3`

`A = 2, B = 1/2, C = pi/3, D = 3`

Amplitude `= |A| =` NONE for csc function.

Period `= (2pi)/|B| = (2pi) /( 1/2) = 4 pi`

Phase Shift `= -C / B = (-pi/3) / (1/2) = -(2 pi) / 3`, `color(brown)((2 pi) / 3` to the LEFT.

Vertical Shift `= D = 3`

graph{2 cos (x/2 - pi/3) + 3 [-10, 10, -5, 5]}