What are the components of the vector between the origin and the polar coordinate $(9, \frac{5 π}{8})$ $(9, (5pi)/8)$ ?

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Answer 1 · 2018-02-27T06:09:55

Rectangular coordinates are $x = 2.3294, y = 8.6933$ $color(brown)(x = 2.3294, y = 8.6933)$

$r = 9, θ = \frac{5 π}{12}$ $r = 9, theta = (5pi)/12$

To find the rectangular coordinates.

enter image source here

From the above image, we know $x = r cos θ, y = r sin θ$ $x = r cos theta, y = r sin theta$

Therefore, $x = 9 \cdot cos (\frac{5 π}{12}) = 2.3294$ $x = 9 * cos ((5pi)/12) = 2.3294$

$y = 9 \cdot sin (\frac{5 π}{12}) = 8.6933$ $y = 9* sin ((5pi)/12) = 8.6933$

What are the components of the vector between the origin and the polar coordinate (9, (5pi)/8)(9,5π8)(9, (5pi)/8)?