What is the polar form of $( -7,-1 )$ ?

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Answer 1 · 2017-07-06T00:41:09

$(sqrt50,3.28)$

To convert this to a polar coordinate $(r, theta)$ , you can use the following formulas and substitute $-7$ for $x$ and $-1$ for $y$ .

$r^2 = x^2 + y^2$
$tan theta = (y)/(x)$

$r^2 = (-7)^2 + (-1)^2$
$r^2 = 49 + 1$
$r^2 = 50$
$r = sqrt50$

$tan theta = (y)/(x)$
$tan theta = (-1)/(-7)$
$theta = tan^-1(1/7)$
$theta ~~ 0.14$

Since the coordinate is in quadrant $"III"$ , we must add $pi$ to this for the correct angle:

$= 0.14 + pi ~~ 3.28$

Thus, the polar form of $(-7,-1)$ is $(sqrt50,3.28)$ .

Answer 2 · 2017-07-06T00:48:55

$(sqrt(50), 3.283)$ (in radians)

The polar form of a rectangular coordinate is given by

$r = sqrt(x^2 + y^2)$

$theta = arctan(y/x)$

So,

$r = sqrt((-7)^2 + (-1)^2) = color(red)(sqrt(50)$

$theta = arctan((-1)/(-7)) = 0.142$ $"rad"$ $+ pi = color(blue)(3.283$ $color(blue)("rad"$

$pi$ was added because the coordinate is in the third quadrant.

The polar form is thus

$(color(red)(sqrt(50)), color(blue)(3.283))$

What is the polar form of ( -7,-1 )( -7,-1 )?