Question

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

Answer 1

`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.`