Question

What are the components of the vector between the origin and the polar coordinate `(14, (5pi)/12)`?

Answer 1

Horizontal component `x=3.623` units.
vertical component `y=13.523` units.

Explanation:

To convert polar form `(r,theta)` into rectangular components `(x,y)` we use the transformations :

`x=rcostheta and y=rsintheta`.

So in this particular case we get

`x=14cos((5pi)/12)=3.623`

`y=14sin((5pi)/12)=13.523`

So the vector may be represented in rectangular form as `3.623hati+13.523hatj`.