If`x=3sint-sin3t ,y=3cos t-cos3t ,"f i n d"(dy)/(dx)"a t"t=pi/3dot`

1.	If`x=3sint-sin3t ,y=3cos t-cos3t ,"f i n d"(dy)/(dx)"a t"t=pi/3dot`
Answer» `x = 3sint-sin3t` `:. dx/dt = 3cost-3cos3t = 3(cost-cos3t)` `y= 3cost - cos3t` `:. dy/dt = -3sint +3sin3t = 3(sin3t-sint)` Now, `dy/dx = (dy/dt)/(dx/dt) = (3(sin3t - sint))/(3(cost-cos3t))` At `t = pi/3`, `dy/dx = (3(0-sqrt3/2))/(3(1/2+1)) = (-sqrt3/2)/(3/2) = -1/sqrt3` `:. dy/dx\|_(t = pi/3) = -1/sqrt3.`

Discussion

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