Quiz/Worksheet #9 MAT 308 - 1
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1. Graph the curves and find the area it encloses:
(a) r= sin(3θ) (b) #5 on pp. 683 of the text
(c) r2= 4 cos(2θ) (d) #8 on pp. 683 of the text
2. Find the area of the region that lies in the first curve and outside the second curve:
(a) r= 3 cos(θ) and r= 1 + cos θ
(b) The area inside the larger loop and outside the smaller loop of the lima¸con r=1
2+cos θ
3. Find the exact length of the polar curves:
(a) r= 3 sin θfor 0 ≤θ≤π/3
(b) r=θ2for 0 ≤θ≤2π
4. Find the slope of the tangent line to the given polar curve at the point specified by the
value of θ:
(a) r= 1/θ at θ=π(b) r= 3 cos θat θ=π/3
(c) r= sin θ+ cos θat θ=π/2 (d) r=eθat θ=π/4