How do you convert $(-8,0)$ into polar forms?

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Answer 1 · 2018-05-05T18:28:55

$(8, pi)$ (radians) or $(8, 180^@)$ (degrees)

Rectangular $->$ Polar: $(x, y) -> (r, theta)$

Find $r$ (radius) using $r = sqrt(x^2 + y^2)$
Find $theta$ by finding the reference angle: $tantheta = y/x$ and use this to find the angle in the correct quadrant

$r = sqrt((-8)^2 + (0)^2)$

$r = sqrt(64)$

$r = 8$

Now we find the value of $theta$ using $tantheta = y/x$ .

$tantheta = 0/-8$

$tantheta = 0$

$theta = tan^-1(0)$

$theta = 0 or pi$

To determine which one it is, we have to look at our coordinate $(-8, 0)$ . First, let's graph it:
enter image source here

As you can see, it is on the negative side of the $x$ axis. Our $theta$ has to match where that is, meaning that $theta = pi$ .

From $r$ and $theta$ , we can write our polar coordinate:
$(8, pi)$ (radians) or $(8, 180^@)$ (degrees)

Hope this helps!

How do you convert (-8,0)(-8,0) into polar forms?