Question

Part 6 of 10 - Negative and positive Values for Trig Functions Dacia wonders how, given the Cartesian coordinates of a point, she can determine the polar coordinate r. Which of Katarina's responses is correct? O "Use the formula r = x + y." "Use the formular = x2 + y2." O "Use the formula r = x2 + y2." "Use the formula 0 - tan Submit Skip you cannot come back)

Answer 1

In polar coordinates(r,$\theta$), r denotes the distance of the given point from the origin and $\theta$ denotes the angle the vector to that point is making with the positive X axis.

Now, using distance formula, we know that the distance of a point (x,y) from the origin is (x^2+y^2)^0.5.

So, r=(x^2+y^2)^0.5

Hence,third option is correct and first and second options are wrong.

Now, note that $\theta$ can vary from 0 degrees to 360 degrees. But the range of inverse tangent function(tan-1) is -90 degrees to +90 degrees. So,$\theta$​​​​​​ =tan-1(y/x) won't be correct for second and third quadrants. So,fourth option is wrong.

So,correct answer is third option.