Please help me simplify a derivative

aarunt1 · 2007-01-16 20:38:41

The problems is x = 3cos^3(3t)

I got dx/dt = -27sin(3t)cos^2(3t)

I need to simplify this. I tried a few identities but I can't get it simpler and I know there is someway to do it. Someone please help me! Thanks

Snow · 2007-01-16 22:02:24

no I believe that it. Unless their is something i'm missing, then that is the final answer.

aarunt1 · 2007-01-16 23:29:15

There has to be a way to simplify it with identities. This is from a parametric equation problem. I already solved and simplified the y= equation, I just need this one.

Last edited by aarunt1 (2007-01-16 23:29:45)

mathsyperson · 2007-01-17 00:47:40

Simplify it how? Do you want it in terms of t instead of 3t? If so, then it's possible, but the result will probably be a lot more complicated than that one.

You need to use the two addition identities:

sin(A+B) ≡ sinAcosB + cosAsinB
cos(A+B) ≡ cosAcosB - sinAsinB

By substituting A=2t, B=t into those, you can convert the 3t's into 2t's and t's, and then by using A=B=t you can convert the 2t's into t's.

The equation will probably look really messy and horrible once you've done that though.

aarunt1 · 2007-01-17 07:22:08

Well the problem is The problems is x = 3cos^3(3t) , y=4sin^2(2t) and it wants to know the length of the curve. It seems impossible without dx/dt simplifying down to something small and I figured it should be possible since I can simplify dy/dt

bobbym · 2011-10-10 18:01:22

Hi;

Long time ago!

Just an alternate form.

Math Is Fun Forum

#1 2007-01-16 20:38:41

Please help me simplify a derivative

#2 2007-01-16 22:02:24

Re: Please help me simplify a derivative

#3 2007-01-16 23:29:15

Re: Please help me simplify a derivative

#4 2007-01-17 00:47:40

Re: Please help me simplify a derivative

#5 2007-01-17 07:22:08

Re: Please help me simplify a derivative

#6 2011-10-10 18:01:22

Re: Please help me simplify a derivative

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