It is 1:08 AM and I am trying to solve some problems but I am stuck :) Can I get some help please? Thanks!

enter image source here

1 Answer
Apr 15, 2018

See below.

Explanation:

If we express the cosine function in the following way:

y=acos(bx+c)+d

Then:

\ \ \bba \ \ \ ="the amplitude"

bb((2pi)/|b|) \ \="the period"

bb((-c)/b)= "the phase shift"

\ \ \ \bbd \ \ \="the vertical shift"

a)

For given function we have:

b=(2pi)/|3|

We know from above that:

"period"=(2pi)/|b|

Hence:

(2pi)/((2pi)/3)=color(blue)(3)

b)

From above:

"amplitude" =a=color(blue)(1/4)

c)

The midline is a line that runs between the maximum and minimum values of the function.

These max/min values are the same as the amplitude, remember amplitude is given as an absolute value:

|a|

We can see from the function written in the form:

y=acos(bx+c)+d

that there is no vertical shift. i.e d=0. This means the midline is just the x axis. This is the same as for cos(theta)

color(blue)(y=0)

The graph confirms our findings:

enter image source here