Question

What are the components of the vector between the origin and the polar coordinate `(10, (7pi)/6)`?

Answer 1

Components are `-5sqrt3` along `x` axis and `-5` along `y` axis.

Explanation:

Components of a vector between the origin and the polar coordinate `(r,theta)` can be written as `(rcostheta, rsintheta)`, where `rcostheta` is the component along `x` axis and `rsintheta` is the component along `y` axis.

Hence, components of a vector between the origin and the polar coordinate `(10,(7pi)/6)` are

`10cos(7pi/6)` or `10*(-cospi/6)` i.e. `10*-sqrt3/2`

or `-5sqrt3` along `x` axis

`10sin(7pi)/6` or `10*(-sinpi/6)` i.e. `10*-1/2`

or `-5` along `y` axis