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

2 Answers
Fleur · Nathan L.
Jul 6, 2017

(sqrt50,3.28)(√50,3.28)

Explanation:

To convert this to a polar coordinate (r, theta)(r,θ), you can use the following formulas and substitute -7−7 for xx and -1−1 for yy.

r^2 = x^2 + y^2r2=x2+y2
tan theta = (y)/(x)tanθ=yx

r^2 = (-7)^2 + (-1)^2r2=(−7)2+(−1)2
r^2 = 49 + 1r2=49+1
r^2 = 50r2=50
r = sqrt50r=√50

tan theta = (y)/(x)tanθ=yx
tan theta = (-1)/(-7)tanθ=−1−7
theta = tan^-1(1/7)θ=tan−1(17)
theta ~~ 0.14θ≈0.14

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

= 0.14 + pi ~~ 3.28=0.14+π≈3.28

Thus, the polar form of (-7,-1)(−7,−1) is (sqrt50,3.28)(√50,3.28).

Nathan L.
Jul 6, 2017

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

Explanation:

The polar form of a rectangular coordinate is given by

r = sqrt(x^2 + y^2)r=√x2+y2

theta = arctan(y/x)θ=arctan(yx)

So,

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

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

piπ was added because the coordinate is in the third quadrant.

The polar form is thus

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

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