# Differentiating with parametric equations

• March 18th 2012, 06:52 AM
johnreal
Differentiating with parametric equations
For part of my parametric eqn i need to differentiate 3-2cos2 theta, when i do this i get 2-sin2 theta, but the answers says 4sin2 theta, what am i doing wrong(Wondering)
• March 18th 2012, 06:58 AM
princeps
Re: Differentiating with parametric equations
Quote:

Originally Posted by johnreal
For part of my parametric eqn i need to differentiate 3-2cos2 theta, when i do this i get 2-sin2 theta, but the answers says 4sin2 theta, what am i doing wrong(Wondering)

$(3-2\cos \2\theta)'=3'-(2\cdot (\cos \2\theta)'+2' \cdot \cos \2 \theta)=$

$= 0-(-4\cdot \sin \2 \theta +0)= 4 \cdot \sin 2 \theta$
• March 18th 2012, 07:18 AM
johnreal
Re: Differentiating with parametric equations
Thanks alot this helped *slaps face* Product Rule, ive worked out most of it and ive reached sin2 theta/cos theta, i did that by having 4sin2 theta/4cos theta and cancelling the fours, im supposed to get 2 sin theta, did i do some thing wrong?
• March 18th 2012, 07:27 AM
princeps
Re: Differentiating with parametric equations
Quote:

Originally Posted by johnreal
Thanks alot this helped *slaps face* Product Rule, ive worked out most of it and ive reached sin2 theta/cos theta, i did that by having 4sin2 theta/4cos theta and cancelling the fours, im supposed to get 2 sin theta, did i do some thing wrong?

$\sin 2\theta = 2 \sin \theta \cdot \cos \theta$