Question

What are the components of the vector between the origin and the polar coordinate `(-1, (7pi)/12)`?

Answer 1

The components of vector between origin & the point `(r, \theta)\equiv(-1, {7\pi}/12)` along the coordinate axes x& y respectively are given as follows

`r\cos\theta=-1\cos({7\pi}/12)=\frac{\sqrt3+1}{2\sqrt2}=0.25881904510252085`

`r\sin\theta=-1\sin({7\pi}/12)=-\frac{\sqrt3-1}{2\sqrt2}`
`=-0.9659258262890683`