wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If x=acost+t sint and y=asint-t cost, then find the value of d2ydx2 at t=π4.

Open in App
Solution

We have,x=acost+t sint and y=asint-t costOn differentiating with respect to t, we getdxdt=ddtacost+t sint=-asint+asint+atcost =atcostanddydt=ddtasint-t cost=acost-acost+atsint =atsintNow, dydx=dydtdxdt=atsintatcost=tantd2ydx2=ddxdydx=ddxtant =ddttant×dtdx=sec2t×1atcost =1atcos3td2ydx2t=π4=1aπ4cos3π4=82aπHence, at t=π4, d2ydx2=82aπ.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Extrema
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon