What are the polar coordinates of $(3, 4)$ $(3, 4)$ ?

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What are the polar coordinates of $(3, 4)$ $(3, 4)$ ?

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Answer 1 · 2014-09-13T04:15:46

When converting from rectangular coordinates to polar coordinates you use the following 2 formulas.

$x^{2} + y^{2} = r^{2}$ $x^2+y^2=r^2$ AND $θ = {tan}^{- 1} (\frac{y}{x})$ $theta=tan^-1(y/x)$

Using the values for the ordered pair you make the necessary substitutions for $x and y$ $x and y$ .

$3^{2} + 4^{2} = r^{2}$ $3^2+4^2=r^2$
$9 + 16 = r^{2}$ $9+16=r^2$
$25 = r^{2}$ $25=r^2$
$\sqrt{25} = \sqrt{r^{2}}$ $sqrt(25)=sqrt(r^2)$
$\pm 5 = r$ $+-5=r$

$θ = {tan}^{- 1} (\frac{y}{x}) = {tan}^{- 1} (\frac{4}{3}) = {53.13}^{o}$ $theta=tan^-1(y/x)=tan^-1(4/3)=53.13^o$

Solution:

Polar coordinates are in the form $(r, θ) \to (\pm 5, {53.13}^{o})$ $(r,theta) ->(+-5,53.13^o)$

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