How do you convert the Cartesian coordinates (-1,1) to polar coordinates?

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Answer 1 · 2018-05-05T18:34:43

$(sqrt2, (3pi)/4)$ (radians) or $(sqrt2, 135^@)$ (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

$r = sqrt((-1)^2 + (1)^2)$

$r = sqrt(1+1)$

$r = sqrt2$

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

$tantheta = -1/1$

$tantheta = -1$

$theta = tan^-1(-1)$

$theta = (3pi)/4$ or $(7pi)/4$

To determine which one it is, we have to look at our coordinate $(-1, 1)$ . First, let's graph it:
enter image source here

As you can see, it is in the secondquadrant. Our $theta$ has to match that quadrant, meaning that $theta = (3pi)/4$ .

From $r$ and $theta$ , we can write our polar coordinate:
$(sqrt2, (3pi)/4)$ (radians) or $(sqrt2, 135^@)$ (degrees)

Hope this helps!