Question

Find rectangular coordinates of the polar coordinates (3,-2) Find the polar coordinates of the rectangular coordinates (2, 5pi/4)

Answer 1

See below

Explanation:

I'm assuming by your prompt you're looking to convert (3,-2) into polar coordinates and (2, 5pi/4) into rectangular coordinates (assuming θ is in radians and not degrees).

For converting rectangular to polar coordinates, recall
`r=√(x^2+y^2)` and
`\theta=\tan^(-1)((y)/(x))`, therefore,
`r=√(3^2+(-2)^2)=√(9+4)=√(13)` and
`\theta=\tan^(-1)((-2)/(3))\approx-0.588`, making
`(r,\theta)=(√(13),0.588)`

For converting polar to rectangular coordinates, recall
`(x,y)=(r\cos\theta,r\sin\theta)`, therefore,
`(2\cos((5\pi)/(4)),2\sin((5\pi)/(4)))\approx(-√(2),-√(2))`.