Question

What is the period, amplitude, and frequency for `f(x)=3+3 cos (\frac{1}{2}(x-frac{\pi}{2}))`?

Answer 1

Amplitude `= 3`, Period `= 4pi`, Phase shift `= pi / 2`, Vertical shift `= 3`

Explanation:

Standard form of equation is `y = a cos (bx + c) + d`

Given `y = 3 cos ((x/2) - (pi /4) ) + 3`

`:. a = 3, b = (1/2), c = -(pi/4) , d = 3`

Amplitude `= a = 3`

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

Phase shift `= -c / b = (pi/4) / (1/2) = pi / 2`, `color(blue)((pi/2)`to the right.

Vertical shift `= d = 3`

graph{3 cos ((x/2) - (pi / 4)) + 3 [-9.455, 10.545, -2.52, 7.48]}