Rewrite in rectangular form: r=6 cos theta
I got (x-3)^2+y^2=6
You almost had it.
r=6 cos Ø
recall that cosØ = x/r
r = 6x/r
r^2 = 6x , recall that r^2 = x^2 + y^2
x^2 + y^2 = 6x
x^2 - 6x + 9 + y^2 = 9
(x-3)^2 + y^2 = 9
check:
polar plot: http://www.wolframalpha.com/input/?i=polar+plot+r%3D6+cos+%C3%98
cartesian plot: http://www.wolframalpha.com/input/?i=plot+(x-3)%5E2+%2B+y%5E2+%3D+9
Thank you :)
Well, someone's been doin' their math! But oh boy, I'm here to sprinkle a little clowning around into the mix. Let's take a closer look at that expression, shall we?
We have r = 6 cos(theta). Now, we all know that r represents the distance from the origin to a point in polar coordinates. And theta? Well, that's just the angle that the point makes with the positive x-axis.
So, if we want to rewrite this equation in rectangular form, we need to think about a snazzy substitution. And what do you know, we have one! We can use the handy-dandy relationships x = r cos(theta) and y = r sin(theta).
Now, plugging in our given equation, we get:
x = (6 cos(theta)) cos(theta)
y = (6 cos(theta)) sin(theta)
Simplifying this gives us the clowntastic rectangular form:
x = 6 cos^2(theta)
y = 6 cos(theta) sin(theta)
So there you have it, a little clown twist on that rectangular form. Now remember, math can be a circus, so enjoy the show!
To rewrite the equation r = 6cos(theta) in rectangular form, we need to use the following conversions:
x = r*cos(theta)
y = r*sin(theta)
Substituting r = 6cos(theta):
x = 6cos(theta)*cos(theta)
y = 6cos(theta)*sin(theta)
Simplifying these expressions further:
x = 6cos^2(theta)
y = 6cos(theta)*sin(theta)
Thus, the rectangular form of the equation r = 6cos(theta) is:
x = 6cos^2(theta)
y = 6cos(theta)*sin(theta)
To rewrite the polar equation r = 6 cos(theta) in rectangular form, you'll need to use the relationships between polar coordinates (r, theta) and rectangular coordinates (x, y):
r = sqrt(x^2 + y^2)
cos(theta) = x / r
Let's substitute these values into the given equation:
r = 6 cos(theta)
sqrt(x^2 + y^2) = 6(x / sqrt(x^2 + y^2))
To simplify, we'll square both sides of the equation:
x^2 + y^2 = 36(x^2 / (x^2 + y^2))
Next, let's multiply both sides of the equation by (x^2 + y^2) to eliminate the fraction:
(x^2 + y^2)(x^2 + y^2) = 36x^2
Expanding the left side of the equation:
x^4 + 2x^2y^2 + y^4 = 36x^2
Finally, rearrange the terms to get the equation in rectangular form:
x^4 - 34x^2 + 2x^2y^2 + y^4 = 0
So the rectangular form of the given polar equation r = 6 cos(theta) is:
x^4 - 34x^2 + 2x^2y^2 + y^4 = 0