How do you find the polar coordinate for (-4, -4)?

Question

6201 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-05T18:50:08

$(4sqrt2, (5pi)/4)$ (radians) or $(4sqrt2, 225^@)$ (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

$r = sqrt((-4)^2 + (-4)^2)$

$r = sqrt((16)+16)$

$r = sqrt(32)$

$r = sqrt(16*2)$

$r = 4sqrt2$

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

$tantheta = (-4)/(-4)$

$tantheta = 1$

$theta = tan^-1(1)$

$theta = (pi)/4$ or $(5pi)/4$

To determine which one it is, we have to look at our coordinate $(-4, -4)$ . First, let's graph it:
enter image source here

As you can see, it is in the third quadrant. Our $theta$ has to match that quadrant, meaning that $theta = (5pi)/4$ .

From $r$ and $theta$ , we can write our polar coordinate:
$(4sqrt2, (5pi)/4)$ (radians) or $(4sqrt2, 225^@)$ (degrees)

Hope this helps!