Question

Convert the polar coordinates (-3, -60°) to Cartesian coordinates.

Answer 1

(1.5,-2.6)

Explanation:

Given the polar coordinates (-3,60°).

Let our Cartesian coordinates be (x,y)

#We know that when converting the rectangular coordinates (x,y) to polar (r,θ), then:

`r=√(x^2+y^2)\\\\\therefore r^2=x^2+y^2\\\\\theta=tan^(-1)(y/x)\\\therefore tan \theta=y/x`

#Using the illustration above, we can express our polar coordinates as:

`-3=√(x^2+y^2)\\\\-60\textdegree=tan^(-1)(y/x}`

#Solve simultaneously to solve for x and y:

`(-3)^2=x^2+y^2\ \ \ \ \ \ \ \ \ \ i\\\\tan(-0\texdegree)=y/x\ \ \ \ \ \ \ \ ...ii\\\\y=x\ tan(-60\textdegree)\ \ \ \ \ \ \ ...iii\\\\\#substitute\ y \ in\ i\\\\(-3)^2=x^2+(x \ tan (-60\textdegree))^2\\\\9=x^2+3x^2\\\\x=√(9/4)=1.5\\\\y=1.5\ tan(-60\textdegree)=-2.5981\approx-2.6`

Hence, the Cartesian coordinates are (1.5,-2.6)