For the given point in rectangular coordinates, how do you find the corresponding polar coordinates for the point $(10 \sqrt{3}, 10)$ $(10 sqrt (3), 10)$ ?

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For the given point in rectangular coordinates, how do you find the corresponding polar coordinates for the point $(10 \sqrt{3}, 10)$ $(10 sqrt (3), 10)$ ?

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Answer 1 · 2016-06-10T10:46:23

$(20, \frac{π}{6})$ $(20,pi/6)$

Explanation:

To convert from (x ,y) to $(r, θ)$ $(r,theta)$ use the formulae which connect Cartesian to Polar coordinates.

$∙ r = \sqrt{x^{2} + y^{2}}$ $•r=sqrt(x^2+y^2)$

$∙ θ = {tan}^{- 1} (\frac{y}{x})$ $•theta=tan^-1(y/x)$

here x $= 10 \sqrt{3} and y = 10$ $=10sqrt3" and "y=10$

$\Rightarrow r = \sqrt{{(10 \sqrt{3})}^{2} + 10^{2}} = \sqrt{300 + 100} = \sqrt{400} = 20$ $rArrr=sqrt((10sqrt3)^2+10^2)=sqrt(300+100)=sqrt400=20$

and $θ = {tan}^{- 1} (\frac{10}{10 \sqrt{3}}) = {tan}^{- 1} (\frac{1}{\sqrt{3}}) = \frac{π}{6}$ $theta=tan^-1(10/(10sqrt3))=tan^-1(1/sqrt3)=pi/6$

$\Rightarrow (10 \sqrt{3}, 10) \to (20, \frac{π}{6})$ $rArr(10sqrt3,10)→(20,pi/6)$

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For the given point in rectangular coordinates, how do you find the corresponding polar coordinates for the point $(10 \sqrt{3}, 10)$ $(10 sqrt (3), 10)$ ?

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Explanation:

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For the given point in rectangular coordinates, how do you find the corresponding polar coordinates for the point $(10 \sqrt{3}, 10)$ $(10 sqrt (3), 10)$ ?