Question

How do you convert the polar point `(6,120^o)` into rectangular form?

Answer 1

The rectangular coordinates are `=(-3, 3sqrt3)`

Explanation:

We use the following equations to convert from polar coordinates `(r,theta)` to rectangular coordinates `(x,y)`

`x=rcostheta`

`y=rsin theta`

Therefore,

`x=6cos120`º `=-6*1/2=-3`

and `y=6sin120`º `=6*sqrt3/2=3sqrt3`

So the rectangular coordinates are `=(-3, 3sqrt3)`

Answer 2

`(-3,3sqrt3)`

Explanation:

To convert from `color(blue)"polar to rectangular form"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(x=rcostheta , y=rsintheta)color(white)(2/2)|)))`

here r = 6 and `theta=120^@`

`rArrx=6cos120^@=-6cos60^@=-6xx1/2=-3`

and `y=6sin120^@=6sin60^@=6xxsqrt3/2=3sqrt3`

`rArr(6,120^@)=(-3,3sqrt3)`