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12. Since the graph has 5 'petals', the period of the function is 2 pi/5, and the answer is C.
13. To find the area, use the formula in polar coordinates:
A = (1/2)∫0π/2 r2(θ)dθ = (1/2)∫0π/2 sin2(2θ)dθ = use the identity sin2x = (1 – cos 2x)/2
(1/4)∫0π/2 (1 – cos(4θ))dθ = (¼) (θ – ¼ sin(4θ)) ] 0π/2 = π/8.
The answer is D.
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