Question

Find a cartesian equation for the curve described by the given polar equation.
a. r=2
b. r=3sin pheta
c.r^2=sin2pheta

I don't understand how to solve for this, especially for r squared. Would someone plz explain how o convert to a cartesian equation. any help would be greatly appreciated!

Answer 1

The relationships you need should be in your text, or you can find them at the top of
http://mathworld.wolfram.com/PolarCoordinates.html

your first one r = 2 is then quite easy

r = √(x^2 + y^2)

2 = √(x^2 + y^2)
x^2 + y^2 = 4 which is a circle

your second:

r=3sin pheta
r=3sinß

but sinß = y/r
r=3sinß
r = 3(y/r)
r^2 = 3y
x^2 + y^2 = 3y

for the third I can't tell if you mean

r^2 = sin(2ß) or r^2 = sin²ß

I will let you decide and then follow my previous examples.