Question

What are the components of the vector between the origin and the polar coordinate `(-1, (pi)/6)`?

Answer 1

The minus 1 flips the point `180^o` from Quadrant I to Quadrant III ...

Explanation:

So, `(-1, pi/6) = (1,(7pi)/6)`

Using a Unit Circle (since `r=1`), `x=-sqrt3/2` and `y=-1/2`

Therefore, the endpoint of the vector is `(-sqrt3/2, -1/2)`

Finally, the components of a vector starting at the origin and ending at `(-sqrt3/2, -1/2)` is `a=-sqrt3/2` and `b=-1/2` and using the unit vectors `i and j`:

`-sqrt3/2i-1/2j`

or it can just be written as `<-sqrt3/2,-1/2>`