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

x = a (θ – sin θ), y = a(1 + cos θ) at


θ = – π/2

Given:


x = a() & y = a(1 + cos) at


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


(xn) = n.xn – 1


x = a()


= a(() – (sin))


= a(1 – ) ...(1)


(sinx) = cosx


y = a(1 + cos)


= a(() + (cos))


(cosx) = – sinx


(Constant) = 0


= a( + ( – sin))


= a( – sin)


= – asin ...(2)




The Slope of the tangent is


Since,



sin() = 1


cos() = 0




= 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