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How do you convert $(- 5, - 5)$ $(-5, -5)$ into polar form?

1 Answer

Nov 3, 2016

Cartesian: $(x, y) = (- 5, - 5)$ $(x,y)=(-5,-5)$
$XXX$ $color(white)("XXX")$ Polar: $(r, θ) = (5 \sqrt{2}, \frac{5 π}{4})$ $(r,theta)=(5sqrt(2),(5pi)/4)$

Explanation:

$(- 5, - 5)$ $(-5,-5)$ is a point in Quadrant III (since both $x$ $x$ and $y$ $y$ components are negative.

The $x$ $x$ and $y$ $y$ components are equal, so the reference angle is $\frac{π}{4}$ $pi/4$ .
If the reference angle is $\frac{π}{4}$ $pi/4$ and the angle is in Q III,
then the angle is $π + \frac{π}{4} = \frac{5 π}{4}$ $pi+pi/4=(5pi)/4$

The radius is the length of the hypotenuse; with an angle of $\frac{π}{4}$ $pi/4$ the length of the hypotenuse is $\sqrt{2} \times | length of side |$ $sqrt(2) xx abs("length of side")$

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