How do you write the equation using rectangular coordinates given $r^{2} sin 2 θ = 8$ $r^2sin2theta=8$ ?

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Answer 1 · 2016-10-04T09:50:27

$x y = 4$ $xy=4$

The relation between rectangular Cartesian coordinates $(x, y)$ $(x,y)$ and polar coordinates $(r, θ)$ $(r,theta)$ is given by

$x = r cos θ$ $x=rcostheta$ , $y = r sin θ$ $y=rsintheta$ and $x^{2} + y^{2} = r^{2}$ $x^2+y^2=r^2$

Hence $r^{2} sin 2 θ = 8$ $r^2sin2theta=8$ can be rewritten as

$r^{2} \times 2 sin θ cos θ = 8$ $r^2xx2sinthetacostheta=8$

or $2 \times r sin θ \times r cos θ = 8$ $2xxrsinthetaxxrcostheta=8$

or $2 \times y \times x = 8$ $2xxyxx x=8$

or $x y = 4$ $xy=4$

How do you write the equation using rectangular coordinates given r^2sin2theta=8r2sin2θ=8r^2sin2theta=8?