Asked by Jessica
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!
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!
Answers
Answered by
Reiny
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 = sin<sup>2</sup>ß
I will let you decide and then follow my previous examples.
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 = sin<sup>2</sup>ß
I will let you decide and then follow my previous examples.