# How do you convert (8.3, 4.2) into polar forms?

Jan 29, 2016

$\left(9.302 , 0.149 \pi\right)$

#### Explanation:

suppose,
$x = 8.3$
$y = 4.2$
now, we know,
for polar form,
${r}^{2} = {x}^{2} + {y}^{2}$

$\mathmr{and} , r = \sqrt[2]{{x}^{2} + {y}^{2}}$

now, by putting the value of x and y in the equation, we get

r=root(2)(8.3^2+4.2^2

$= \sqrt[2]{86.53}$

$= 9.302$

again
we know,
$\theta = {\tan}^{- 1} \left(\frac{y}{x}\right)$

by putting the value of x and y on the above equation, we get,

$\theta = {\tan}^{- 1} \left(\frac{4.2}{8.3}\right)$

$= 0.149 \pi$

so, the polar form is ( $9.302 , 0.149 \pi$)