Question

Which rectangular equation is equivalent to the polar equation r sin theta=-2

Answer 1

The rectangular equation that is equivalent to the given polar equation is:

y= -2

Explanation:

We know that the polar coordinate of a equation are related to the rectangular coordinates of the equation as:

`x=r\sin \theta\\\\y=r\cos \theta`

where,

`r=√(x^2+y^2)`

Now we are given that:

`r\sin \theta=-2`

Also,

`\theta=\arctan (y)/(x)`

Hence, on converting the given polar equation to the rectangular equation we get:

`y=-2`

Answer 2

To convert polar equations in the form of r∠∅ to rectangular coordinates in terms of x, y and r, the formulas are as follows:

r2 = x2 + y2
x = rcos∅
y = rsin∅

Since the equation is rsin∅=y, then rsin∅=-2 is equivalent to y=-2.