Question

How do you express the Cartesian coordinates (3, - 4) as polar coordinates?

Answer 1

Polar Coordinates `(5, 306.86989765^@)`
OR
Polar Coordinates `(5, -53.13010235^@)`

Explanation:

Given: `x=3` and `y=-4`

`r=sqrt(x^2+y^2)=sqrt(3^2+(-4)^2)=sqrt(25)=5`

`theta=tan^-1 (y/x)=tan^-1 (-4/3)=306.86989765^@`

God bless....I hope the explanation is useful.

Answer 2

`(r,theta) = 5 angle -0.927295[radian]`

Explanation:

The pass equations are
`x = r cos(theta)`
`y = r sin(theta)`
and dividing each equation side
`y/x=tan(theta)` and also its inverse function
`theta = arctan(y/x)`
also `x^2+y^2=r^2cos(theta)^2+r^2sin(theta)^2 = r^2(cos(theta)^2+sin(theta)^2)=r²`
Applying all those formulas we get
`3^2+(-4)^2=r^2=25 = 5^2`
`theta = arctan(-4/3) =-0.927295[radian]`