Find the equation for a cosine wave

[Rose1234]

The question is ‘write an equation for a cosine wave that passes through the ordered pairs (0,5),(4,12),(8,5),(12,-2),(16,5).

 

[MarkFL]

Hello, and welcome to FMH!

Let's plot the given points first:



From this, can you more easily identify the amplitude, vertical shift, phase shift, and period?

 

[Rose1234]

Thank you so much! It is easy to do it with the points graphed but I was wondering whether it is possible to find the equation without having to draw out the coordinates?

 

[Otis]

The question is: write an equation for [the] cosine wave that passes through the ordered pairs (0,5), (4,12), (8,5), (12,-2), (16,5).

You didn't follow the forum's submission guidelines, so my question is: Are you familiar with the sinusoidal form?

y = A∙cos(B[x - C]) + D

It is described at this web page.

If you sketch a quick diagram, you'll see that they've described one period of the cosine wave. All of the numbers you need to determine the parameters A,B,C,D are given.

Please show any work that you've already tried, or ask specific questions. Thanks!

?

 

[Otis]

... It is easy to do it with the points graphed but I was wondering whether it is possible ... without having to draw ...

Oops, I see didn't see the replies, before submitting my previous post.

Regarding your wondering above, one could reason it out using mental images, instead of drawing, or ask a machine to do it.