What is the polar form of $( -18,-6 )$ ?

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Answer 1 · 2017-06-27T19:13:32

$(18.974, 3.463)$

We're asked to find the polar form of a rectangular coordinate.

We can do so by using the equations

$r = sqrt(x^2 + y^2)$

$theta = arctan(y/x)$

The $x$ -coordinate is $-18$ , and the $y$ -coordinate is $-6$ , so

$r = sqrt((-18)^2 + (-6)^2) = color(red)(18.974$

$theta = arctan((-6)/(-18)) = 0.322 + pi = color(blue)(3.463$

The $pi$ was added to fix the calculator error, the coordinate is located in quadrant $III$ . (Remember the angle $theta$ is in radians.)

The polar form of this coordinate is thus

$(color(red)(18.974), color(blue)(3.463))$

What is the polar form of ( -18,-6 )( -18,-6 )?