Question

Write the following equation in polar form.

y=3


r=3sinθ
r=1/3sinθ
r=3cscθ
r=1/3cscθ
r=3cosθ
r=1/3cosθ

Answer 1

Answer:r=3cscθ

Step-by-step explanation:The equation y = 3 represents a horizontal line at a distance of 3 units above the x-axis in the Cartesian coordinate system. To convert this equation into polar form, we can use the fact that x = rcos(theta) and y = rsin(theta) in polar coordinates.

Since y = 3 for all values of x, we can say that r*sin(theta) = 3. Solving for r, we get:

r = 3/sin(theta)

This equation represents a family of circles with center at the origin and radius 3/sin(theta), for all values of theta except for multiples of pi. We can simplify this equation by using the identity sin(theta) = 1/csc(theta), giving us:

r = 3csc(theta)