Transformations on the graph of cosine and sine..

Question

abbles · Answer

My current lesson is about graphing sine, cosine, all the trig functions, and transforming them.  I'm having a bit of trouble when it comes to graphing the transformations.  For instance:

y = sin(3x)

I know that it will be a horizontal stretch of the graph of y = sinx... but how would I graph it?

abbles · Answer

I also have y = cos(1/2x) that I have no clue how to graph...

elusive · Answer

So.. The number in front of x is used to define the period of the graph.

elusive · Answer

Period: $$\frac{ 2 \pi }{ b }$$

elusive · Answer

where the 3 in y=sin(3x) is b.

elusive · Answer

Therefore.. the period for y=sin(3x) would be $$\frac{ 2 \pi }{ 3 }$$

abbles · Answer

Okay, thanks!  What next?

elusive · Answer

Do you know how to sketch the graph in general? All you have to do is mark (2pi/3) and draw one full sin period within that space.

abbles · Answer

Oh okay... I think I can do that.  Is there a formula for finding any of the coordinates or no?

elusive · Answer

In this case, the amplitude is just 1 because there is nothing in front of sin. Therefore the max would be 1 and min would be -1.

abbles · Answer

Gotcha.  What about the zeros?  Would they be the same?

elusive · Answer

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