Question

Convert each of the following equations from polar coordinates to rectangular coordinates. r^2sin(2theta)=4

Answer 1

hint : \(\large \sin(2\theta) = 2\sin \theta \cos\theta\)

Answer 2

do i divide both sides next?

Answer 3

\[\large r^2\sin(2\theta) = r^2\cdot 2\sin\theta \cos\theta = 2(r\sin\theta)(r\cos\theta) = ?\]

Answer 4

\(\large x = r\cos\theta\)
\(\large y = r\sin\theta\)

remember these ?

Answer 5

yes

Answer 6

just plug them in and you're done

Answer 7

\[\large r^2\sin(2\theta) = r^2\cdot 2\sin\theta \cos\theta = 2(r\sin\theta)(r\cos\theta) = 2xy\]

Answer 8

so the rectangular form would be :
\[\large 2xy = 4\]

Answer 9

which is same as
\[\large xy = 2\]