Question

Write a cosine function that has a amplitude of 3, an midline of 5 and a period of pi/2f(x)=

Answer 1

Recall that the general formula of a cosine function is of the form

`A\cdot\cos (Bx-C)+D`

where A is the amplitude, D is the midline, the number C/B is the phase shift and the number 2*pi/B is the period.

We are told that A=3 and D=5. Also, we are told that the period is pi/2. Since we don't have any information regarding the phase shift, we will asume that the phase shift is 0. Then we have the following equations:

`(C)/(B)=0`

and

`(2\cdot\pi)/(B)=(\pi)/(2)`

From the first equation we deduce that C should be zero. From the second equation by multiplying by B on both sides and dividing by pi on both sides, we get

`2=(B)/(2)`

If we multiply by 2 on both sides, we get

`B=2\cdot2=4`

so gathering our previous results, we get the formula

`3\cos (4x)+5`