Question

Draw a graph of the rose curve. r = -3 sin 5θ, 0 ≤ θ ≤ 2π A) a graph of five loops originating at the origin where one loop lies on and is symmetric about the bottom part of the y axis and each of the four remaining loops lie in each quadrant, one, two, three, and four [-4, 4] by [-4, 4]

Answer 1

The rose curve graph for r = -3 sin 5θ will have five loops with one loop symmetric about the bottom part of the y-axis and the other four loops distributed in each quadrant, fitting within a coordinate scale of [-4, 4].

Step-by-step explanation:

The question involves drawing a graph of a rose curve with the polar equation r = -3 sin 5θ, where θ ranges from 0 to 2π. To graph a rose curve, we use polar coordinates where the length r represents the distance from the origin to a point on the curve, and the angle θ represents the direction from the positive x-axis to the line connecting the origin to that point. In the equation given, 5 indicates the number of petals or five loops that the rose curve will have.

When graphing the equation, one loop will lie along and be symmetric to the negative y-axis (since r is negative when θ is 0), and the other four will be distributed across the four quadrants of the coordinate system. The graph's scale can be set to [-4, 4] by [-4, 4] in both the x and y directions to ensure that the full extent of the rose curve is visible. The resulting graph should appear as a five-petaled flower centered at the origin of the polar coordinate system.