Question

Are there more than one way to convert Polar to Rectangular coordinates?

Answer 1

All Polar `rarr` Rectangular coordinate conversions are based on the definitions of `sin` and `cos`:
`color(white)("XXX")sin(theta)=y/rcolor(white)("XXX")cos(theta)=x/r`

Explanation:

There may be many ways to visualize the conversion of Polar to Rectangular coordinates. Sometimes (depending upon the values of `r` or `theta`) it is easier or faster to see this conversion graphically or in some other form, but in the end it comes back to the relationship between `x, y, r, and theta` as defined by the trigonometric functions.

(I assume here that we are dealing only with Real values of `x, y, r, and theta`).