The area of one loop of the rose curve defined by the polar equation r = cos(3θ) can be determined using double integrals. The limits for θ are established as -π/6 and π/6 because these values correspond to the points where r equals zero, specifically at θ = -π/6 (where 3θ = -π/2) and θ = π/6 (where 3θ = π/2). This range effectively encloses one complete loop of the curve, as r remains non-zero within these bounds. Understanding these limits is crucial for accurately calculating the area using the appropriate integral setup.
PREREQUISITESStudents studying calculus, particularly those focusing on polar coordinates and integration techniques, as well as educators teaching these concepts in mathematics courses.