convert to rectangular form r=12sintheta-16costheta

Question

zepdrix · Answer

Recall that when switching between rectangular and polar we use:$$\Large\rm x=r \cos \theta,\qquad\qquad y=r \sin \theta$$

zepdrix · Answer

$$\Large\rm r=12\sin \theta-16\cos \theta$$Multiplying each side by r gives us,$$\Large\rm r^2=12r \sin \theta-16 r \cos \theta$$

anonymous · Answer

i'm at x^2+y^2=12y-16y

anonymous · Answer

err 16x

zepdrix · Answer

$$\Large\rm x^2+y^2=12y-16x$$Ok great.
Move everything to the left side,$$\Large\rm x^2+16x+y^2-12y=0$$And from here we'll want to complete the square on the x's and y's.

anonymous · Answer

so it'd be (x+8)^2+(y-6)^2=64+36?

zepdrix · Answer

64 for the x's,
36 for the y's,
?

Mmm yes very good.
Looks like you've got it figured out! :)

anonymous · Answer

oh... it's that simple?

zepdrix · Answer

Yah they're not too bad.
Sometimes they'll make you do some weird stuff with square roots.
But for the most part, if you can remember your identities that let you switch,
and completing the square (which you seem to be very good at), then they're not too much trouble.

anonymous · Answer

ok thanks