What are the components of the vector between the origin and the polar coordinate #(14, (5pi)/12)#?

1 Answer
Trevor Ryan.
Jan 13, 2016

Horizontal component #x=3.623# units.
vertical component #y=13.523# units.

Explanation:

To convert polar form #(r,theta)# into rectangular components #(x,y)# we use the transformations :

#x=rcostheta and y=rsintheta#.

So in this particular case we get

#x=14cos((5pi)/12)=3.623#

#y=14sin((5pi)/12)=13.523#

So the vector may be represented in rectangular form as #3.623hati+13.523hatj#.

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