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sec10_4

# sec10_4 - r = 4 sin 3 θ Example 1.3(problem 24 ±ind the...

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10.4 Areas and Lengths in Polar Coordinates 1. Area Recall from trigonometry: The area of the sector of a circle with radius r and radian measure of central angle θ is A = 1 2 r 2 θ. Theorem 1.1. The area of the region within the sector a θ b enclosed by the curve r = f ( θ ) is given by Example 1.1. (problem 10) Sketch the curve r = 3(1 + cos θ ) and find the area that it encloses. Example 1.2. (problem 18) Find the area of the region enclosed by one loop (petal) of the curve

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Unformatted text preview: r = 4 sin 3 θ . Example 1.3. (problem 24) ±ind the area of the region that lies inside the curve r = 1-sin θ and outside the cirve r = 1 . 1 Section 10.4 Areas and Lengths in Polar Coordinates 2 2. Arclength Recall x = r cos θ , y = r sin θ , and ds = ± ( dx ) 2 + ( dy ) 2 . So ds = Example 2.1. (problem 46) Find the exact length of the polar curve r = e 2 θ , ≤ θ ≤ 2 π...
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