Question

What is the Cartesian form of `( 12, (-7pi)/2 )`?

Answer 1

So Cartesian coordinate=`(0,12)`

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=12 and theta =-7pi/2`
`x= 12*cos(-7pi/2)= 12*cos(7pi/2)= 12*sin(4pi-pi/2)`
`=12cos(pi/2)=0`
`y= 12*sin(-7pi/2)= -12*cos(7pi/2)`
`= -12*sin(4pi-pi/2)=12sin(pi/2=12`

So Cartesian coordinate=`(0,12)`