Consider a point with rectangular coordinates (x, y). If x<0 then the polar coordinates of the point are (r,θ) where r≥0 and −π/2≤θ<3π/2and:

r=

θ=

If x≥0 then the polar coordinates of the point are (r,θ) where r≥0 and −π/2≤θ<3π/2 and:

r=

θ=​

Step-by-step explanation:

I see a major problem with this question in that the possible range for θ is VERY narrow...mostly because -π/2 = 3π/2

That would lead to θ = -π/2 and force x = 0 and y = r and make the whole situation a rather moot question.

IF we ASSUME that it is supposed to be  π/2 ≤ θ ≤ 3π/2

THEN I would suggest that θ = π + arctan(y/x) radians

We need to add π to get the result into the second or third quadrants

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

answer: b

step-by-step explanation: