What are the components of the vector between the origin and the polar coordinate $(8, \frac{11 π}{12})$ $(8, (11pi)/12)$ ?

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Answer 1 · 2018-02-27T05:49:36

Rectangular coordinates are $x = - 7.7274, y = 2.0706$ $x = -7.7274, y = 2.0706$

Given Polar coordinates $(r, θ) - (8, \frac{11 π}{12})$ $(r,theta) - (8,(11pi)/12)$

To find rectangular coordinates $(x, y)$ $(x,y)$

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$x = r cos θ = 8 \cdot cos (\frac{11 π}{12}) = - 7.7274$ $x = r cos theta = 8 * cos ((11pi)/12) = -7.7274$

$y = r sin θ = 8 \cdot sin (\frac{11 π}{12}) = 2.0706$ $y = r sin theta = 8 * sin ((11pi)/12) = 2.0706$

$tan (\frac{y}{x}) tan θ = tan (\frac{11 π}{12}) = - 0.2679$ $tan (y/x) tan theta = tan ((11pi)/12 )= -0.2679$

What are the components of the vector between the origin and the polar coordinate (8,11π12)(8, (11pi)/12)?