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Question

If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t) then find dydxat t=π4.


Solution

x=asin2t(1+cos2t),y=bcos2t(1cos2t)dydx=2acos2t(1cos2t)+asin2t(2sin2t)=2acos2t+2acos22t2asin22t=2acos2t+2acos4tdydx=2bsin2t(1cos2t)+bcos2t(2sin2t)=2bsin2t+2bsin2tcos2t+2bcos2tsin2t(2sin2t)=2bsin2t+4bsin2tcos2t=2bsin2t+2bsin4t dydtdxdt=2b sin 2t+2b sin 4t2a cos 2t+2a cos 4tdydt=2b sin 2t+2b sin 4t2a cos 2t+2a cos 4tdydtt=π4=2b sin2π4+2b sin 4π42a cos2π4+2a cos4π4dydtt=π4=2b sinπ4+2b sin π2a cos π2+2a cosπdydtt=π4=2b2a=badydtt=π4=ba

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