Question

What is the Cartesian form of `( 5 , ( - 15pi)/4 )`?

Answer 1

`(0,5)`

Explanation:

If Cartesian or rectangular coordinate of a point be (x,y)
and its polar polar coordinate be `(r,theta)`

then `x=rcostheta and y= rsintheta`
here `r=5 and theta =-15pi/2`
`x= 5*cos(-15pi/2)=5cos(15pi/2)=5cos(8pi-pi/2)=5*cos(pi/2)=0`
`y= 5*sin(-15pi/2)=-5sin(15pi/2)=-5sin(8pi-pi/2)=5*sin(pi/2)=5`
So Cartesian coordinate=`(0,5)`