Final answer:
The length of the petals of the rose graph given by the polar equation r = 8cos(3θ) is 30°.
Step-by-step explanation:
To find the length of the petals of the rose graph given by the polar equation r = 8cos(3θ), we need to find the value of θ at which r = 0 (the value of θ where the curve crosses the x-axis). When r = 0, 8cos(3θ) = 0, which means cos(3θ) = 0. This happens when 3θ = 90°, 270°, 450°, etc (or in general, when 3θ = (2n + 1)90° where n is an integer). So, the angle at which the curve crosses the x-axis is θ = (2n + 1)30°. Since we are interested in the length of the petals, we need to find the difference in θ between two consecutive points on the x-axis. This can be found by subtracting the θ values at two consecutive points on the x-axis. The difference in θ values is 30°. Therefore, the length of each petal is 30°.