prirodnogbk

2022-07-10

What is the polar form of $\left(11,-9\right)$ ?

Gornil2

Expert

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The polar form of a coordinate pair $\left(x,y\right)$ is $\left(r,\theta \right)$
To find r, we use the formula ${r}^{2}={x}^{2}+{y}^{2}$
math xmlns="http://www.w3.org/1998/Math/MathML"> r 2 = 11 2 + ( - 9 ) 2
${r}^{2}=121+81$
${r}^{2}=202$
$r=\sqrt{202}$
$r\approx 14.21$
To find $\theta$ , we use the formula $\frac{y}{x}=\mathrm{tan}\left(\theta \right)$
$\frac{-9}{11}=\mathrm{tan}\left(\theta \right)$
$\theta ={\mathrm{tan}}^{-1}\left(\frac{-9}{11}\right)$
$\theta \approx {\mathrm{tan}}^{-1}\left(0.818182\right)$
$\theta \approx -39.289407$

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