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HW9sol - MAC1114 Homework 9 Due Thursday March 17 1 Find...

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Unformatted text preview: MAC1114 - Homework 9 Due Thursday - March 17 1. Find the asymptotes (do not nd periods or sketch graphs) of the following functions: (a) 2 csc(3 x- π 2 ) Period: 2 π b = 2 π 3 Asymptotes: 3 x- π 2 = nπ ⇒ 3 x = nπ + π 2 ⇒ x = nπ 3 + π 6 , n ∈ Z (b) sec( π 3 x + π 2 ) + 3 Period: 2 π b = 2 π π 3 = 6 Asymptotes: π 3 x + π 2 = nπ + π 2 ⇒ π 3 x = nπ ⇒ x = 3 n , n ∈ Z (c) 1 2 tan( 2 5 x- π ) Period: π b = π 2 5 = 5 2 π Asymptotes: 2 5 x- π = nπ + π 2 ⇒ 2 5 x = nπ + π 2 ⇒ x = 5 nπ 2 x + 5 π 4 , n ∈ Z (d)- cot(7 x- 3) Period: π b = π 7 Asymptotes: 7 x- 3 = nπ ⇒ x = nπ +3 7 , n ∈ Z 2. In the gure below (not shown here) , a square is inscribed in another square, and then a circle is inscribed in the smaller square. Point P is the center of the circle. The area of the larger square is 100. Find the area of the region shaded blue. Since the area of the larger square is 100, each side has length 10. Half of this is 5, so the short sides of the right triangles formed in each corner of the larger square both have length 5. From the Pythagoreanthe right triangles formed in each corner of the larger square both have length 5....
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