Q. 1 G4.7( 3 Votes )

# 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))

= 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

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