rectangular form to polar form
xy=12
rsinÆŸ rcosÆŸ=12
would the answer be:
r^2=12/cosÆŸ sinÆŸ
please show steps,
Thanks
Yes, if you mean
r^2 = 12/ (sinØcosØ)
you could also change it to
r^2 = 24/sin(2Ø) , (recall sin2Ø = 2sinØcosØ )
To convert an equation from rectangular form to polar form, we can use the trigonometric identities:
1. Start with the given equation in rectangular form: xy = 12.
2. Express x and y in terms of polar coordinates:
x = r * cos(θ) (where r represents the radial distance and θ represents the angle)
y = r * sin(θ)
3. Substitute these expressions for x and y in the equation:
r * cos(θ) * r * sin(θ) = 12
r² * cos(θ) * sin(θ) = 12
4. Rearrange the equation to solve for r²:
r² = 12 / (cos(θ) * sin(θ))
5. This is the polar form of the given equation: r² = 12 / (cos(θ) * sin(θ))
So, your answer is correct:
r² = 12 / (cos(θ) * sin(θ)).