What is the polar form of $(1, 18)$ $(1,18)$ ?

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Answer 1 · 2016-06-01T20:36:43

$(r, θ) = (5 \sqrt{13}, arctan (18))$ $(r,theta)=(5sqrt(13),arctan(18))$

Given Cartesian coordinates $(x, y)$ $(x,y)$ in Quadrant I

$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$
and
$θ = arctan (\frac{y}{x})$ $theta=arctan(y/x)$

Answer 2 · 2016-06-01T20:49:20

(18, 1.5)

Polar format: (r, $θ$ $theta$ )

$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$

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

apply both formulas when going from Cartesian -> polar

$\sqrt{1^{2} + 18^{2}} = \sqrt{325} \approx 18.0$ $sqrt(1^2+18^2) = sqrt(325) ~~ 18.0$

$θ = {tan}^{- 1} (\frac{18}{1}) = {tan}^{- 1} (18) \approx 1.5 r a d i a n s$ $theta = tan^-1(18/1) = tan^-1(18) ~~ 1.5 radians$

Thus our answer of:

Polar format of (1,18) Cartesian is:

(18, 1.5)

What is the polar form of (1,18)(1,18)(1,18)?