convert to polar: 2xy=3
A. r=sqrt(3sin theta cos theta)
B. r=sqrt[(3sin theta cos theta)/2]
C. r=[3/(2sin theta cos theta)]
D.This cannot be converted without ambiguity.
plug and chug:
2xy = 3
2 rcosθ rsinθ = 3
so, (C)
To convert the equation 2xy = 3 to polar coordinates, you can follow these steps:
1. Replace x and y with their polar coordinate equivalents:
- x = rcos(theta)
- y = rsin(theta)
2. Substitute these values into the given equation:
2(rcos(theta))(rsin(theta)) = 3
3. Simplify the equation:
2r^2cos(theta)sin(theta) = 3
4. Divide both sides by 2:
r^2cos(theta)sin(theta) = 3/2
5. Divide both sides by cos(theta)sin(theta):
r^2 = (3/2) / (cos(theta)sin(theta))
6. Take the square root of both sides:
r = sqrt[(3/2) / (cos(theta)sin(theta))]
Therefore, the correct answer is option B: r = sqrt[(3sin(theta)cos(theta))/2].