Find the period of the given function.

Question

y = (7/2)cos 6x

Answer 1

Latika,

 

What is the period of a trig function? Trig functions all repeat the same values over and over again. They do so over an interval, otherwise known as the period.

 

For instance, cos(x) repeats its values over interval lengths of 2π. Look at the graph of cos(x). See that from 0 to 2π on the x-axis, the y-values make a distinct pattern as they go from 1 back to 1. They start again at x=2π and end at it x=4π. See? They keep doing that. They do it every 2π.

 

What about your function? How could you create the graph that would allow you to identify the period?

 

The way I do this is to sort of "recreate" one of the intervals of the original function, which is cos(x) in your case. I do this by looking at what are usually the easiest points to take cos(x) of: 0, π/2, π, 3π/2, and 2π.

 

Now I can't just plug each of these into cos(6x). Rather, I want the argument of cos(6x) to equal each of these. By argument, I mean the thing inside the parentheses. That is, I want to make 6x equal to each of 0, π/2, π, 3π/2, and 2π.

 

Here's how to do it, by example. I'll make the argument equal π/2. That is, I'll set 6x = π/2. So x=π/12.

 

Now try that for the rest of the points and make the graph. Does that look like the graph of cos(x)? How has it been changed? Is that consistent with what you know about how multiplying a function by 6 should stretch or condense that function?

 

Best of luck,

Bryce