What is the period of the function g(x) = sin (6px)?

Question

What is the period of the function g(x) = sin (6πx)?

Answer 1

Start with the knowledge that the period of the function f(x) = sin (x) is 2π.  That means that the function repeats over and over, every 2π.

 

Then, when you multiply x in the function definition by some number, you DIVIDE the period by that number.  So for example, the period of sin (2x) = 2π / 2 = π.

 

In this case, you are multiplying x by 6π, so you divide 2π by 6π to get the period.  The result is 1/3.

 

 

Answer 2

The period of a function is how long it takes the curve to start repeating itself...or how long it takes to complete 1 curve. It is related to the frequency. the frequency answers the question how many curves are in 2π. The frequency is always found as the coefficient of the x in y = cos 3x or y = sin 5x.

so in y = cos 3x, the frequency is 3 which means 3 curves in 2π. if you divide by 3 you get 1 curve in 2π/3.

In the second example, y=sin 5x, the frequency is 5, meaning 5 curves in 2π or 1 curve in 2π/5.

 

So your example has a frequency of 6π, meaning 6π curves in 2π. Divide both by 6π and you get 1 curve in 1/3. So your period is 1/3.

 

Hope this helped.