Question

What are the components of the vector between the origin and the polar coordinate `(-4, (pi)/6)`?

Answer 1

`2√3` along `x` axis and `2` along `y` axis

Explanation:

In polar coordinates `(r, theta)`, r is always positive and quadrants are changed using angle `theta`. I presume what you mean is polar coordinates `(4, pi/6)`.

Components of a vector coordinate `(r, theta)` and origin are `rcostheta` along `x` axis and `rsintheta` along `y` axis.

Hence these are `4cos(pi/6)` along `x` axis and `4sin(pi/6)` along `y` axis.

i.e. `2 sqrt3` along `x` axis and `2` along `y` axis.