Question

Consider a polar graph with a curve r=f(θ). The question ask me to find a point farthest from the initial line.

The method the examiner use is to rewrite the equation in the form y=f(θ)h(θ) and differentiating the equation with respect to θ. Equate the derivative to 0 and work out the θ.

Why are we supposed to convert r=f(θ) to y=f(θ)h(θ)? Can't we just find the derivative of r with respect to θ and equate it to 0 to work out the value?

Answer 1

@ganeshie8 @Irishboy123

Answer 2

what is meant by initial line?

Answer 3

θ=0

Answer 4

ah ok. Then the question is about your perpendicular distance (height) from that line I'm guessing.

Answer 5

you can have a maximal radius and still not be the furthest point from the line

Answer 6

just curious what h(theta) did they provide you?

Answer 7

@mww Not the perpendicular distance. Perpendicular distance is the shortest distance. They are asking about the point at which the distance is furthest

Answer 8

f(x) = a/(1+θ)
h(x) =sin θ

h(x) is simply the converter used when converting r into y
y= r sin θ

Answer 9

I am supposed to make an equation which outputs values of θ at which distance is maximum.

Answer 10

well that makes a lot of sense.

you are required to find the maximum for y (the vertical height of the point from the fixed line) so you'd differentiate y = r sin(theta)

Answer 11

of course your r is a variable in this situation

Answer 12

Oh I got it. I was confusing radius with farthest point from initial line.

Answer 13

The point here is that the maximum you find for r may NOT necessarily be the maximum for y

Answer 14

yeah radius is distance from a point, the origin, specifically