What is the polar form of ( -11,121 )?

Dec 22, 2016

$\left(r , \theta\right) \approx \left(121.50 , 1.66\right)$

Explanation:

The radius can be calculated using the Pythagorean Theorem as
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{r} = \sqrt{{\left(\textcolor{red}{- 11}\right)}^{2} + {\textcolor{red}{121}}^{2}} \approx 121.4989712$

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$\tan \left(\textcolor{b l u e}{\pi}\right) = \frac{121}{- 11} = - 11$

The standard $\text{arctan}$ function gives us the reference angle in either Quadrant I or Quadrant IV (in Q IV in this case since the value of the "tan" is negative).

$\arctan \left(- 11\right) \approx - 1.48013644$ (radians)

$\theta = \pi + \arctan \left(- 11\right) \approx 1.661456214$