SOLUTION: If f(x) = cosx, write a function g(x) for the sinusoid that translates f(x) with the following transformations: Reflected over the midline y=-3, with an amplitude of 3, twice th

Algebra ->  Trigonometry-basics -> SOLUTION: If f(x) = cosx, write a function g(x) for the sinusoid that translates f(x) with the following transformations: Reflected over the midline y=-3, with an amplitude of 3, twice th      Log On


   

Question 1115522: If f(x) = cosx, write a function g(x) for the sinusoid that translates f(x) with the following transformations:
Reflected over the midline y=-3, with an amplitude of 3, twice the period, and a phase shift of pi/2 to the right.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The general cosine function is

a%2Acos%28b%28x-c%29%29%2Bd

a is the amplitude;
b determines the period (the period is 2pi/b);
c is the horizontal phase shift; and
d is the vertical shift.

"reflected..." -- that means a is negative

"...over the midline y=3..." -- that's a vertical shift; d is 3

"...with an amplitude of 3..." -- we already know a is negative; now this means a is -3

"...twice the period..." -- the period is 4pi; since the period is 2pi/b, b is 1/2

"...and a phase shift of pi/2 to the right -- that means c is pi/2

Put it all together, using the values of a, b, c, and d you have determined:

-3%2Acos%28%281%2F2%29%28x-pi%2F2%29%29%2B3