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Unformatted text preview: les and their Measure 609 9. Consider the circle of radius r pictured below with central angle θ, measured in radians, and
subtended arc of length s. Prove that the area of the shaded sector is A = 1 r2 θ.
2 s r
r HINT: Use the proportion: A
area of the circle
circumference of the circle 10. Use the result of Exercise 9 to compute the areas of the circular sectors with the given central
angles and radii.
(a) θ = π
, r = 12
6 (b) θ = 5π
, r = 100
4 (c) θ = 330◦ , r = 9.3 11. Imagine a rope tied around the Earth at the equator. Show that you need to add only 2π feet
of length to the rope in order to lift it one foot above the ground around the entire equator.
(You do NOT need to know the radius of the Earth to show this.)
12. With the help of your classmates, look for a proof that π is indeed a constant. 610 Foundations of Trigonometry 10.1.3 Answers 1. (a) 63◦ 45 (b) 200◦ 19 30 (c) −317◦ 3 36 (d) 179◦ 59 56 2. (a) 125.833◦ (b) −32.17◦ (c) 502.583◦ (d)...
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