Question

On the interval [0, 2π), which points are intersections of r=5sin(θ) and r=−6sin(θ)? Check all that apply..

a. (−3, 7π/6​)
b. (−3, 11π/6​)
c. (3, 5π/6​)
d. (3, 7π/6​)
e. (3, 11π/6​)

Answer 1

To find the points of intersection between the polar curves r=5sin(θ) and r=-6sin(θ) on the interval [0, 2π), set the two equations equal to each other and solve for θ. The points of intersection are (0, 0), (π, 0), and (2π, 0).

Step-by-step explanation:

The given problem involves finding the points of intersection between two polar curves, r=5sin(θ) and r=-6sin(θ), on the interval [0, 2π). To find the points of intersection, you can set the two equations equal to each other:

5sin(θ) = -6sin(θ)

Now, you can solve for θ:

11sin(θ) = 0

sin(θ) = 0

θ can take on values of 0, π, and 2π on the given interval. To find the corresponding points in polar coordinates, substitute these θ values back into one of the original equations. After evaluating, the points of intersection are (0, 0), (π, 0), and (2π, 0).