determine whether the function is periodic?if it is periodic,find the smallest (fundamental) period.

a) sin x - cos [(2)^1/2]x

Question

determine whether the function is periodic?if it is periodic,find the smallest (fundamental) period.

a) sin x - cos [(2)^1/2]x

alfie · Answer

This function is not periodic, so we have no period.

anonymous · Answer

how u know that its not periodic?teach me please..

anonymous · Answer

$$\sin x - \cos \sqrt{2}x$$

alfie · Answer

http://tutorial.math.lamar.edu/Classes/DE/PeriodicOrthogonal.aspx Try to read this, is quite easy to understand.

anonymous · Answer

ouh..then how about this?
$$\cos 3x-\sin 7x$$

alfie · Answer

Both sine and cosine are periodic in your last function, a sum of two periodic functions is a periodic function

anonymous · Answer

hmm..can u explain in detail..im sorry if im asking too much..

alfie · Answer

$$\cos3x - sen7x = \cos(3x+T) - \sin(7x + T)$$

We know that both cosine and sine period happens to be $$2\pi$$
You try to plug in $$2\pi$$ inside of the given function and you'll see you'll have the very same value, since it makes a 360° spin and comes back to the starting point.

anonymous · Answer

meaning that when we substitute T to $$2\pi$$ it will give the same answer..is that what u mean?

alfie · Answer

Yes, as a simple example. $$\sin(90°)$$ is eqaul to 1. 
Now, if you do:
$$\sin(90°) = \sin(90° + T) \rightarrow \sin(90°) = \sin(90° + 360°)$$
Obviously the period of the sin is 360°, so is 
sin of 360°+90 = sin90° ?
Try it yourself, how much is $$\sin(450°)$$ ?
If it is 1 as well, we have a periodic function.

anonymous · Answer

ouhh..now i understand..thank u so much for helping me !! ^^,

alfie · Answer

You're welcome :)

anonymous · Answer

^^,

anonymous · Answer

alfie how come you say sin x - cos (sqrt x ) is not periodic?

alfie · Answer

Take a look at the graph.