How do you find the polar coordinates given the rectangular coordinates (1,sqrt3)?

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How do you find the polar coordinates given the rectangular coordinates (1,sqrt3)?

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Answer 1 · 2017-04-24T08:24:18

$(1, \sqrt{3})$ $(1, sqrt(3))$ in rectangular coordinates is $(2, \frac{π}{3})$ $(2, pi/3)$ in polar coordinates.

Explanation:

To translate rectangular to polar coordinates we use the follow:
$x = r cos (θ)$ $x=r cos(theta)$
$y = r sin (θ)$ $y=r sin(theta)$

From your question we can set up the equations:
$1 = r cos (θ)$ $1=r cos(theta)$
$\sqrt{3} = r sin (θ)$ $sqrt(3)=r sin(theta)$

Solve these simultaneous equations by division first:
$\frac{\sqrt{3}}{1} = \frac{sin (θ)}{cos (θ)}$ $sqrt(3)/1 = sin(theta)/cos(theta)$
$\sqrt{3} = tan (θ)$ $sqrt(3) = tan(theta)$
$θ = \frac{π}{3}$ $theta = pi/3$

Now substitute to find $r$ $r$ :
$1 = r cos (\frac{π}{3})$ $1=r cos(pi/3)$
$1 = r \frac{1}{2}$ $1=r 1/2$
$2 = r$ $2=r$

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How do you find the polar coordinates given the rectangular coordinates (1,sqrt3)?

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