Question

How do you convert `(1, (3pi )/ 4)` into cartesian form?

Answer 1

`"Polar: "(r,theta)=(1,(3pi)/4)color(white)("XX")rarrcolor(white)("XX")color(green)("Cartesian: "(x,y)=(-1/sqrt(2),1/sqrt(2))`

Explanation:

An angle of `(3pi)/4` is equivalent to a reference angle of `pi/4` in the second Quadrant.

Here is a fairly standard image of this relationship

However the polar coordinates tell us that the radius (hypotenuse) needs to be `1`,
so all sides need to be scaled down by dividing by `sqrt(2)`
giving x-coordinate: `-1/sqrt(2)` and y-coordinate: `1/sqrt(2)`