What are the components of the vector between the origin and the polar coordinate #(12, (7pi)/8)#?

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What are the components of the vector between the origin and the polar coordinate #(12, (7pi)/8)#?

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Answer 1 · 2016-02-29T03:58:10

( #-#12 cos #pi#/8, 12 sin #pi#/8 ) =
( #-#6#sqrt#(2 + #sqrt#2 ). 6#sqrt#(2 #-# #sqrt#2 )
= ( #-#11.09, 4.59 ), nearly.

Explanation:

Components of radius vector to ( r, #theta# ) are ( r cos #theta#, r sin #theta# )
cos (#pi# - #theta# ) = #-# cos #theta#
sin (#pi# - #theta# ) = sin #theta#
cos #pi#/8 = #sqrt#((1 + cos #pi#/4)/2)
sin #pi#/8 = #sqrt#((1 #-# cos #pi#/4)/2)

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What are the components of the vector between the origin and the polar coordinate #(12, (7pi)/8)#?

1 Answer

Explanation:

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