SUMMARY
The area enclosed by one leaf of the three-leaved rose defined by the polar equation r = sin(3θ) is calculated using the formula A = 1/2 ∫ r² dθ. The correct limits of integration are from 0 to π/3, leading to the result A = π/12. This conclusion is confirmed as accurate within the discussion.
PREREQUISITES
- Understanding of polar coordinates and their equations
- Familiarity with integral calculus
- Knowledge of trigonometric identities, specifically sin(3θ)
- Experience with definite integrals and area calculations
NEXT STEPS
- Study the derivation of the area formula for polar coordinates
- Explore the properties of rose curves and their equations
- Learn about the application of trigonometric identities in integration
- Practice solving integrals involving trigonometric functions
USEFUL FOR
Students studying calculus, particularly those focusing on polar coordinates and area calculations, as well as educators looking for examples of polar integration techniques.