Hi
I want to find the area of a segment. I know that the area of a segment is given by
But how do I find the area when r isn't constant? e.g when r goes from 1.85 to 1.89
Is it just a case of integrating the equation for area between the two rs?
Thanks
Hello Shizzle
Welcome to Math Help Forum!You are on the right lines. In polar coordinates, the position of a point P is fixed by its distance, , from a fixed point O and the angle, , that the line OP makes with a fixed line.
If a curve is defined by giving as a function of , then the area enclosed between the curve and the rays and isGrandad
Thanks, I'm not sure if I made myself clear enough. The reason I'm asking this question is because I have some results from an experiment I need to analyse.
From to 180 degrees every 15 degrees I measured r.
Although r changes with , the extent to which it changes depends on which 15 degree increment it is measured over.
E.g from 0 to 15 degrees r changed from 1.95 to 1.92, but from 15 to 30 degrees r changed from 1.92 to 1.82.
Don't I need to use these values of r to calculate the area instead of the angle?
Hello ShizzleSince you're working with numerical data, you'll only get an approximation to the area. So I think the best and simplest option is probably to take the mean value of in each ( radians) range, and use with that value. Provided the change in isn't too dramatic in any given range, that should give a good approximation to the area.
So, with the values you mention, the areas of the first two sectors are (approximately):andYou'll be able to simplify it a little by factorising, taking out , to get:
Grandad