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Unformatted text preview: Gauthier, Joseph – Homework 1 – Due: Sep 11 2007, 3:00 am – Inst: JEGilbert 1 This printout should have 17 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. YES, homework 1 is due AFTER homework 2 001 (part 1 of 1) 10 points Express the function f ( x ) = 5 sin 2 x 4 cos 2 x in terms of cos 2 x . 1. f ( x ) = 1 2 + 9 2 cos 2 x 2. f ( x ) = 9 + 1 2 cos 2 x 3. f ( x ) = 9 2 1 2 cos 2 x 4. f ( x ) = 9 2 9 2 cos 2 x 5. f ( x ) = 1 2 9 2 cos 2 x correct 6. f ( x ) = 1 2 9 cos 2 x Explanation: Since sin 2 x = 1 2 (1 cos 2 x ) and cos 2 x = 1 2 (1 + cos 2 x ) , we can rewrite f as f ( x ) = 5 2 (1 cos 2 x ) 2(1 + cos 2 x ) . Consequently, f ( x ) = 1 2 9 2 cos 2 x . keywords: 002 (part 1 of 1) 10 points Simplify the expression f ( θ ) = √ 1 cos 4 θ , eliminating the radical. 1. f ( θ ) = √ 2 sin 2 θ 2. f ( θ ) = √ 2  cos 2 θ  3. f ( θ ) = 2 cos 2 8 θ 4. f ( θ ) = 2 sin 2 8 θ 5. f ( θ ) = √ 2 cos 2 θ 6. f ( θ ) = √ 2  sin 2 θ  correct Explanation: By the double angle formula cos 2 x = 1 2 sin 2 x. With x = 2 θ , therefore, we see that √ 1 cos 4 θ = p 2 sin 2 2 θ . Consequently, f ( θ ) = √ 2  sin 2 θ  , the absolute value being included to ensure that f ( θ ) ≥ 0. keywords: trig identity, simplify trig expres sion, double angle formula 003 (part 1 of 1) 10 points When 1 2 3 1 2 3 1 2 3 Gauthier, Joseph – Homework 1 – Due: Sep 11 2007, 3:00 am – Inst: JEGilbert 2 is the graph of y = a + b cos mx, ( m > 0) , on [ 4 , 4], what is b ? 1. b = 2 2. b = 4 3. b = 7 4 4. b = 4 5. b = 2 correct Explanation: As 1 2 3 1 2 3 1 2 3 shows, the given graph is that of y = 3 2 + 2 cos 1 2 πx, in other words, the graph of y = 2 cos 1 2 πx shifted vertically by a term y = 3 2 . Thus b is given by b = 2 . keywords: graph, trig function, phase, ampli tude, period, vertical shift 004 (part 1 of 3) 10 points The figure ABCD in A C B D θ a b is a parallelogram and BD is a diagonal. (i) Express the area of ABCD as a function of a, b and θ . 1. Area ABCD = 1 2 ab cos θ 2. Area ABCD = 1 2 ab sin θ 3. Area ABCD = ab cos θ 4. Area ABCD = 2 ab sin θ 5. Area ABCD = ab sin θ correct Explanation: In the parallelogram ABCD the triangles Δ ABD and Δ BDC are congruent by SSS since side BD is common to both triangles, while side AD is congruent to side BC and side AB is congruent to side DC . Thus Area ABCD = Area ABD + Area BDC = 2 Area ABD ....
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 Fall '07
 Gilbert
 Trigonometry, Derivative, Cos, Gauthier

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