Question

Which rectangular equation is equivalent to the polar equation r csc theta=8?

Answer 1

The polar equation r csc theta=8 can be converted to the rectangular equation y=8/sin theta.

Step-by-step explanation:

The polar equation r csc theta=8 can be converted to a rectangular equation using the following steps:

Use the identity csc theta = 1/sin theta to replace csc theta in the equation.

Multiply both sides of the equation by r to isolate the variable r.

Replace rsin theta with y and rcsc theta with 1/sin theta in the equation.

After simplifying, the rectangular equation is y = 8/sin theta.

Answer 2

Rectangular and polar forms are two forms of equations that translates to plot. In this case, the two forms are convertible to each other by the expressions:

r sin theta = y
r cos theta = x
x2 + y2 = r2

we are given the polar expression r csc theta = 8 and is asked to convert to rectangular form.

in this case, csc theta is equal to 1/ sin theta. thys
r / sin theta = 8

in order to make use of the equations above, then

we multiply r to both numerator and denominator in the left side, that is
r^2 / r sin theta = 8
x2+y2 / y = 8
x 2 + y2 = 8y