Question

How does one convert polar equations to rectangular form given; angle = 7pi/4 and r(sin of angle) = 7?

Answer 1

`y=-x`

Explanation:

.

The formulas for conversion are:

`y=rsintheta`

`x=rcostheta`

`x^2+y^2=r^2cos^2theta+r^2sin^2theta=r^2(cos^2theta+sin^2theta)=r^2(1)=r^2`

`y=rsin((7pi)/4)=-sqrt2/2r`

`x=rcos((7pi)/4)=sqrt2/2r`

`y/x=(-sqrt2/2r)/(sqrt2/2r)=-1`

`y=-x`

This is the equation of a straight line.