Question

What are the components of the vector between the origin and the polar coordinate `(-3, (11pi)/6)`?

Answer 1

`-\frac{3\sqrt3}{2}\hat i+3/2\hat j`

Explanation:

x & y components of vector `(r, \theta)\equiv(-3, {11\pi}/6)` are given as

`x=r\cos\theta`

`=-3\cos({11\pi}/6)`

`=-3\cos(2\pi-{\pi}/6)`

`=-3\cos({\pi}/6)`

`=-3\frac{\sqrt3}{2}`

`=-\frac{3\sqrt3}{2}`

`y=r\sin\theta`

`=-3\sin({11\pi}/6)`

`=-3\sin(2\pi-{\pi}/6)`

`=3\sin({\pi}/6)`

`=3\frac{1}{2}`

`=\frac{3}{2}`

Hence the vector is

`=-\frac{3\sqrt3}{2}\hat i+3/2\hat j`