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

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

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Answer 1 · 2018-05-05T18:34:43

$(\sqrt{2}, \frac{3 π}{4})$ $(sqrt2, (3pi)/4)$ (radians) or $(\sqrt{2}, 135^{\circ})$ $(sqrt2, 135^@)$ (degrees)

Explanation:

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

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

$r = \sqrt{{(- 1)}^{2} + {(1)}^{2}}$ $r = sqrt((-1)^2 + (1)^2)$

$r = \sqrt{1 + 1}$ $r = sqrt(1+1)$

$r = \sqrt{2}$ $r = sqrt2$

Now we find the value of $θ$ $theta$ using $tan θ = \frac{y}{x}$ $tantheta = y/x$ .

$tan θ = - \frac{1}{1}$ $tantheta = -1/1$

$tan θ = - 1$ $tantheta = -1$

$θ = {tan}^{- 1} (- 1)$ $theta = tan^-1(-1)$

$θ = \frac{3 π}{4}$ $theta = (3pi)/4$ or $\frac{7 π}{4}$ $(7pi)/4$

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

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

From $r$ $r$ and $θ$ $theta$ , we can write our polar coordinate:
$(\sqrt{2}, \frac{3 π}{4})$ $(sqrt2, (3pi)/4)$ (radians) or $(\sqrt{2}, 135^{\circ})$ $(sqrt2, 135^@)$ (degrees)

Hope this helps!

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

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