Questions: Below is the curve r=1-sin(θ) for 0 ≤ θ ≤ a. Adjust the value of a using the slider provided to complete the graph.

Solution Steps

The graph shows a polar curve with the equation \(r = 1 - \sin(\theta)\). The graph is drawn from \(\theta = 0\) to some angle \(a\). The radial lines are in increments of \(\pi/6\). The circles are in increments of 1. We are given \(a = 0.40\). The graph currently shows a small portion of the curve in red, starting at \(\theta=0\) and extending slightly.

The angle \(a\) is given as 0.40, which is likely in radians. The red portion in the graph spans an angle slightly past the 0 radian mark. This visually corresponds to approximately 0.40 radians.

To complete the graph of \(r = 1 - \sin(\theta)\), we need the angle to go from 0 to \(2\pi\). So, we must set \(a = 2\pi\).

Final Answer