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

1 Answer
Dec 30, 2016

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

Explanation:

Components of a vector between the origin and the polar coordinate #(r,theta)# are #(xcostheta,ysintheta)#.
enter image source here

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.