convert r=6cos(theta) to rectangular coordinates
recall that cosØ = y/r
so r = 6cosØ
r = 6y/r
r^2 = 6y
x^2 + y^2 = 6y <---- a circle
To convert the polar equation r = 6cos(theta) to rectangular coordinates, you can use the following formulas:
x = rcos(theta)
y = rsin(theta)
Here, r represents the distance from the origin to a point, and theta represents the angle that the line connecting the point and the origin makes with the positive x-axis.
In this case, the given polar equation is r = 6cos(theta).
Substituting r = 6cos(theta) into the formulas for x and y, we get:
x = (6cos(theta)) * cos(theta) = 6cos(theta)^2
y = (6cos(theta)) * sin(theta) = 6cos(theta) * sin(theta)
Thus, the rectangular coordinate representation of the polar equation r = 6cos(theta) is:
x = 6cos(theta)^2
y = 6cos(theta) * sin(theta)