Math Problem Statement

Find the area of the part of the circle r=8 sintheta + costheta in the fourth quadrant .

Solution

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Math Problem Analysis

Mathematical Concepts

Polar Coordinates
Integration
Trigonometry

Formulas

A = 1/2 ∫(θ₁ to θ₂) r² dθ
r² = (8sinθ + cosθ)² = 64sin²θ + 16sinθcosθ + cos²θ
sin²θ + cos²θ = 1
2sinθcosθ = sin(2θ)

Theorems

Trigonometric Identities
Polar Area Formula

Suitable Grade Level

Grades 11-12 / Early University