How do you convert $(2, \frac{- 7 π}{6})$ $(2,(-7pi)/6)$ into cartesian form?

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How do you convert $(2, \frac{- 7 π}{6})$ $(2,(-7pi)/6)$ into cartesian form?

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Answer 1 · 2017-05-10T23:05:19

Use $x = r cos θ$ $x=rcostheta$ and $y = r sin θ$ $y=rsintheta$ . Answer: $(- \sqrt{3}, 1)$ $(-sqrt(3),1)$

Explanation:

Original problem: Convert $(2, - \frac{7 π}{6})$ $(2, -(7pi)/6)$ to Cartesian

To convert from polar coordinates to Cartesian form, we use the equations $x = r cos θ$ $x=rcostheta$ and $y = r sin θ$ $y=rsintheta$ .

Since we have $(r, θ)$ $(r,theta)$ , we can simply substitute into the above formulas:
$x = 2 cos (- \frac{7 π}{6})$ $x=2cos(-(7pi)/6)$
Using our unit circle trig values
$x = 2 (- \frac{\sqrt{3}}{2})$ $x=2(-sqrt(3)/2)$
$x = - \sqrt{3}$ $x=-sqrt(3)$

$y = 2 sin (- \frac{7 π}{6})$ $y=2sin(-(7pi)/6)$
Using our unit circle trig values
$y = 2 (\frac{1}{2})$ $y=2(1/2)$
$y = 1$ $y=1$

Therefore our final answer in Cartesian form is: $(- \sqrt{3}, 1)$ $(-sqrt(3),1)$

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How do you convert $(2, \frac{- 7 π}{6})$ $(2,(-7pi)/6)$ into cartesian form?

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Explanation:

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How do you convert $(2, \frac{- 7 π}{6})$ $(2,(-7pi)/6)$ into cartesian form?