Question

The petal P of the rose r = 4cos 5θ that contains a portion of the positive x axis lies between the angles θ = α and θ = β, where α < β. Find the values of α and β and then find the area A of the petal P.

Can someone explain how to find alpha and beta please

Answer 1

As each petal is drawn, r begins at the pole, sweeps out through some range of angles and returns to the pole. So each petal is drawn between zeros. To find all of the values of theta that cross the pole...\[4\cos 5 \theta=0\]\[5\theta=\frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}, \frac{7\pi}{2},...\]\[\theta=\frac{\pi}{10}, \frac{3\pi}{10}, \frac{5\pi}{10}, \frac{7\pi}{10},...\]If you check out the peaks in between each zero... it should give you a good idea which interval contains your petal.

Answer 2

\[\Pi/2 and \Pi/10\]

Answer 3

At theta=0 it starts on the positive x axis... so I would say that petal starts a little before 0 and ends a little after zero... like +/- pi/10