Find the The Slopes of the tangent and the normal to the following curves at the indicated points :

x = a cos3 θ, y = a sin3 θ at θ = π/4

Given:


x = acos3 & y = asin3 at


Here, To find , we have to find & and and divide and we get our desired .


(xn) = n.xn – 1


x = acos3


= a((cos3))


(cosx) = – sinx


= a(3cos3 – 1 – sin)


= a(3cos2 – sin)


= – 3acos2sin ...(1)


y = asin3


= a((sin3))


(sinx) = cosx


= a(3sin3 – 1cos)


= a(3sin2cos)


= 3asin2cos ...(2)




= – tan


The Slope of the tangent is – tan


Since,


= – tan()


= – 1


tan() = 1


The Slope of the tangent at x = is – 1


The Slope of the normal =


The Slope of the normal =


The Slope of the normal =


The Slope of the normal = 1


1