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

1 Answer
BeeFree
Jan 5, 2016

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>#

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