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

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Answer 1 · 2016-03-10T04:13:29

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

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

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