Question

Use technology to convert (4, -2) into approximate polar coordinates. Please hurry!!

Answer 1

Answer:

Option C: (4.47,-0.46)

Step-by-step explanation:

To convert Cartesian coordinates $(x,y)$ into polar coordinates $(r,\theta)$, use the following formulas:

$r=\sqrt{x^{2}+y^{2} }$

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

Therefore:

$r=\sqrt{x^{2} +y^{2}}=\sqrt{4^2+(-2)^2}=\sqrt{16+4}=\sqrt{20}=4.47$

$\theta=tan^{-1}(\frac{y}{x})=tan^{-1}(\frac{-2}{4})=tan^{-1}(-\frac{1}{2})=-0.46$

Because (4,-2) is located in Quadrant II, the angle must also be located in Quadrant II. Therefore, the correct polar coordinate would be (4.47,-0.46)