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

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Answer 1 · 2018-07-22T18:15:56

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

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#