Question

Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of pi/2, and a vertical shift up 3 units.

y =

(I don't have the option to use the characters "/" or "
`\pi`" so they must not be in the answer.

Answer 1

The period will change coefficient of x by 2 pi / pi/2 = 4
and the vertical shift will add 3 so its

sin 4x + 3

Hope this helps

Answer 2

y = sin 4x + 3

Explanation:

A sine function is represented as y = a sin(bx + c) + d

Given values in the question are a = amplitude = 1

period = π/2 = 2π/b

Vertical shift d = 3 units up.

Horizontal shift c = 0

Since 2π/b = π/2

`b=(2\pi )/((\pi )/(2)) =(4\pi )/(\pi )=4`

Now the sinusoidal function will be

y = 1. sin( 4x ) + 3

y = sin 4x + 3