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What are the components of the vector between the origin and the polar coordinate #(5, (7pi)/8)#?

1 Answer

A. S. Adikesavan

Mar 10, 2016

#(-sqrt(1/(2sqrt2)(sqrt2+1)), sqrt(1/(2sqrt2)(sqrt2-1)))#.

Explanation:

The components of the radiius vector to #(r, theta)# are (x, y).
x = r cos #theta# and y = r sin #theta#.
Here, r = 5 and #theta=7pi/8#.

Use #cos (7pi/8) = -cos (pi/8)= -sqrt((1+cos (pi/4))/2)#.
#sin (7pi/8) = sin(pi/8)= sqrt((1-cos (pi/4))/2)#
#cos(pi/4)=sin(pi/4)=1/sqrt2#

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