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

1 Answer
A. S. Adikesavan
Feb 29, 2016

( -12 cos pi/8, 12 sin pi/8 ) =
( -6sqrt(2 + sqrt2 ). 6sqrt(2 - sqrt2 )
= ( -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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