Question

Find the slope of the normal to the curve x=l-asina,
y= bcosto, at theta=Pie
e/2​

Answer 1

Answer:

ANSWER

It is given that x=1−asinθ and y=bcos

2

θ.

∴

dθ

dx

=−acosθ

and

dθ

dy

=2bcosθ(−sinθ)=−2bsinθcosθ

dx

dy

=

(

dθ

dx

)

(

dθ

dy

)

=

−acosθ

−2bsinθcosθ

=

a

2b

sinθ

Therefore, the slope of the tangent at θ=

2

π

is given by,

(

dx

dy

)

θ=

4

π

=

a

2b

Hence, the slope of the normal at θ=

2

π

is given by,

−

slope of the tangent atθ=

4

π

1

=

a

2b

−1

=−

2b

a