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

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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.

$x^2+y^2=r^2$ AND $theta=tan^-1(y/x)$

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

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

$theta=tan^-1(y/x)=tan^-1(4/3)=53.13^o$

Solution:

Polar coordinates are in the form $(r,theta) ->(+-5,53.13^o)$

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