What are the components of the vector between the origin and the polar coordinate $(7, \frac{23 π}{12})$ $(7, (23pi)/12)$ ?

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Answer 1 · 2018-02-27T02:52:38

Rectangular coordinates of $\to V$ $vecV$ $(6.7615, - 0.2679)$ $color(green)((6.7615, -0.2679)$

It’s in the fourth quadrant.

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Given : $r = \sqrt{x^{2} + y^{2}} = 7, θ = \frac{23 π}{12}$ $r = sqrt(x^2 + y^2) = 7, theta = (23pi)/12$

To find rectangular coordinates (x,y)

$x = r cos θ = 7 \cdot cos (\frac{23 π}{12}) θ) = 6.7615$ $x = r cos theta = 7 * cos ((23pi)/12)theta) = color (green)(6.7615$

$y = r sin θ = 7 \cdot sin (\frac{23 π}{12}) θ) = - 1.8117$ $y = r sin theta = 7 * sin ((23pi)/12)theta) = color (green)(-1.8117$

$tan θ = \frac{tan (23 π)}{12} = - 0.2679$ $tan theta = tan (23pi)/12 = color (green)(-0.2679$

What are the components of the vector between the origin and the polar coordinate (7, (23pi)/12)(7,23π12)(7, (23pi)/12)?