Question

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)

Answer 1

The answer to this question is B. (sqrt 2, 315 degrees). This polar coordinate is the only coordinate with its angle in quadrant 4 and a length of √1^2 + (-1)^2 = √2.

Answer 2

Answer:

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