Areas and Arc Lengths in Polar Form

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Presentation transcript:

Areas and Arc Lengths in Polar Form 11.4

Let’s investigate the following… From the area of a sector formula and the small angle formula r2 Dq r1

Examples… Sketch and find the area of one petal of Make a guess! How else will you know if your answer is even reasonable? Need to determine appropriate limits for theta Set up as area in polar form and solve

Example… Find the area between and … Do this in Maple

Examples… 11.4: 5,6,30,33 Areas between intersection curves: -need to determine intersection points -use what you know about areas between graphs

Arc Length Let’s explore where the expression comes from… Examples: 46