Find `(dy)/(dx)`, when `x=a(t+sint) and y=a(1-cost).`

1.	Find `(dy)/(dx)`, when `x=a(t+sint) and y=a(1-cost).`
Answer» We have `x=a(t+sint)rArr (dx)/(dt)=a(1+cost)`, `y=a(1-cost)rArr (dy)/(dt)=a sin t.` `therefore(dy)/(dx)=((dy)/(dt)xx(dt)/(dx))=(asint)/(a(1+cost))=(2a sin(t//2)cos(t//2))/(2a cos^(2)(t//2))=tan.(t)/(2).`

Discussion

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