419,841 views
22 votes
22 votes
Find dy/dx any one
x=acost , y=asint​

User Ian Mc
by
3.2k points

1 Answer

21 votes
21 votes

Answer:


x=a \cos t \implies (dx)/(dt)=-a \sin t


y= a \sin t \implies (dy)/(dt)=a \cos t

Using the chain rule:


\begin{aligned}\implies (dy)/(dx) & =(dy)/(dt) * (dt)/(dx)\\\\& = a \cos t * (1)/(-a \sin t)\\\\& = (a \cos t)/(-a \sin t)\\\\& = - (\cos t)/(\sin t)\\\\& = - \cot t\end{aligned}

User Bob Ensink
by
2.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.