Drawing (not too simple) Cosine waves on the x and y axis.

[harmonie_Best]

I have to draw cosine waves in relation to pattern formation for mathematical biology, for example, I have to plot things similar to these on the x-axis;

cos( 2*pi*x / √5 ) from x= 0 to √5
cos( 3*pi*x / 2 √5 ) from x= 0 to 2√5
cos( 3*pi*x / 2 √(5/6) ) from x=0 to 2√5

And with the y-axis;

cos( pi*y / √2 ) from y= 0 to √2
cos( pi*y / √6 ) from y= 0 to √6

I just can't get the jist of it. I can see what they look like on wolfram alpha, but I won't have access to it in say an exam situation and just can't seem to grasp it when trying to do them.
Are there any convenient ways of being able to quickly and sufficiently learn to do similar cos waves?

Need to know any more info to answer the question just ask =)

Thanks in advance,
J

 

[mtayab1994]

Yes you shrink the domain of study to draw part of the wave and then finish it off because the cosine function is an even function. ( f(x)=f(-x) ). You can also count the derivative and see where it equals zero; that means the tangent line is horizontal or parallel to the x-axis and you will get a convex or concave curve. In addition to that you can also count the derivative of other points to get their slope so it can make it easier for you to draw the diagram.