How can I convert a rectangular coordinate equation to polar form?

Question

I need help with my math hw... again =/

How do I convert -

5x + 6y = -3

to polar form? I know that you need to replace x and y with (r cos(theta)) and (r sin(theta)),

5 (r cos(theta)) + 6(r sin(theta)) = -3

but what do I do now?

I need to have the final equation start with r=

Answer 1

wow, well this makes you sound smart :]

Answer 2

you may convert from oblong to polar making use of the formula: X = R*cos? Y = R*sin? in case you amplify the (y-5)^2 portion of the expression you wrote, you get: X^2 + Y^2 + 25 - 10Y = 25 in case you plug the polar variations of X and Y into this expression, you get: R^2 * cos^2(?) + R^2 * sin^2(?) + 25 - 10R*sin? = 25 ingredient out the R^2 words to get: R^2 *( cos^2(?) + sin^2(?) ) + 25 - 10R*sin? = 25 The cos^2 + sin^2 section is a similar as one, so that you've: R^2 - 10R*sin? = 0 that's a similar as: R = 10sin?

Answer 3

What do you mean? You already did the conversion. What else is the problem asking?

If you need to express it in terms of r, then factor out r and then divide. So r = -3 / (5 cos(t)+6sin(t)).