What are the components of the vector between the origin and the polar coordinate #(16, (7pi)/6)#?

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Answer 1 · 2016-12-30T13:14:10

#(-8sqrt3,-8)# or #-8sqrt3hati-8hatj#,

Components of a vector between the origin and the polar coordinate #(r,theta)# are #(xcostheta,ysintheta)#.
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Here we have #r=16# and #theta=(7pi)/6#

Hence components are #(16cos((7pi)/6), 16sin((7pi)/6))#

or #(16xx(-sqrt3/2),16xx(-1/2))#

or #(-8sqrt3,-8)#

We can also write it as #-8sqrt3hati-8hatj#,

where #hati# and #hatj# are unit vectors along #x#-axis and #y#-axis respectively.