The polar equation of a graph is given below:

r=4/sin(theta)

Give the equation of the line in rectangular coordinates.

If you rotate this graph 40 degrees counterclockwise about the pole, would you add or subtract 40 degrees to θ?

Subtract?

sqrt(x^2+y^2) = 4 [sqrt(x^2+y^2) ]/y

y = 4
(of course :)

add is counterclockwise

So the answer for "Give the equation of the line in rectangular coordinates." is sqrt(x^2+y^2) = 4 [sqrt(x^2+y^2) ]/y?

Or is it the y=4?
Again, that's probably a silly question..

To convert the given polar equation into rectangular coordinates, you can use the following formula:

x = r * cos(theta)
y = r * sin(theta)

In this case, the polar equation is given as r = 4/sin(theta). To convert it into rectangular coordinates, substitute the value of r into the formulas:

x = (4 / sin(theta)) * cos(theta)
y = (4 / sin(theta)) * sin(theta)

Simplifying these expressions, we get:

x = 4 * cos(theta)
y = 4 * sin(theta)

Hence, the equation of the line in rectangular coordinates is:
y = 4 * sin(theta)
or
x = 4 * cos(theta)

Regarding the rotation of the graph, if you rotate it 40 degrees counterclockwise about the pole, you would subtract 40 degrees from the original value of theta.