Mathematics: Which set of polar coordinates describes the same location as the rectangular coordinates (1,-1) a. (-1, 135 degrees) b. (sqrt 2, 315 degrees) c. (1, 45 degrees) d. (sqrt 2, 225 degrees)

108Step-by-step explanation:...

Which set of polar coordinates describes the same

maddielr17

14.03.2022

The polar coordinate is $(\sqrt{2},315^\circ)$

B is correct

Step-by-step explanation:

Given:

Rectangular coordinates: (1,-1)

We need to change into polar coordinate.

Cartesian to polar change rule:

$(x,y)\rightarrow (r,\theta)$

$x=r\cos\theta$

$y=r\sin\theta$

$\text{Where, }r=\sqrt{x^2+y^2}\text{ and }\theta=\tan^{-1}\dfrac{y}{x}$

$=r=\sqrt{1+1}=\sqrt{2}$

$\sqrt{2}\cos\theta=1$

$\sqrt{2}\sin\theta=-1$

Cosine is negative and Sine is positive.

Thus, angle lie in IV quadrant.

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

$\theta=360-45=315^\circ$

Cartesian to polar

$(1,-1)\rightarrow (\sqrt{2},315^\circ)$

Hence, The polar coordinate is $(\sqrt{2},315^\circ)$

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