Question

Which polar coordinates represent the same point as the rectangular coordinate (2.-1) ? Select all that apply.

Answer 1

Given:

The rectangular coordinate;

`\begin{gathered} (2,-1) \\ \\ where: \\ x=2 \\ y=-1 \end{gathered}`

To convert to polar coordinate;

`\begin{gathered} (r,\theta) \\ \\ where: \\ r=√(x^2+y^2) \\ \theta=tan^(-1)((y)/(x)) \end{gathered}`

Hence,

`\begin{gathered} r=√(2^2+(-1)^2) \\ r=√(4+1) \\ r=√(5) \\ \\ \\ \theta=tan^(-1)(-(1)/(2)) \\ \theta=-26.565 \\ \theta=-26.6^0 \\ tan\text{ is negative in the second and fourth quadrants} \\ Hence, \\ \\ In\text{ the second quadrant;} \\ \theta=180-26.6 \\ \theta=153.4^0 \\ \\ In\text{ the fourth quadrant;} \\ \theta=360-26.6 \\ \theta=333.4^0 \end{gathered}`

Therefore, as a polar coordinate, (2,-1) is;

`(√(5),333.4^0)\text{ OR }(-√(5),153.4^0)`

Thus, the correct answers are OPTION A and OPTION C.