Question

What is the Cartesian form of `( 6 , ( 9pi)/4 )`?

Answer 1

`(3sqrt2,3sqrt2)`

Explanation:

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

That is `(r,theta)to(x,y)`

`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=(9pi)/4`

`rArrx=6cos((9pi)/4)=6cos((9pi)/4-2pi)`

`=6cos(pi/4)=6xx1/sqrt2=(6sqrt2)/2=3sqrt2`

and `y=6sin((9pi)/4)=6sin((9pi)/4-2pi)`

`=6sin(pi/4)=6xx1/sqrt2=3sqrt2`

`rArr(6,(9pi)/4)to(3sqrt2,3sqrt2)`