154+Exam+Jam+Concise+Problems+Fall+09

154+Exam+Jam+Concise+Problems+Fall+09 - Fall 2009 Exam Jam...

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Fall 2009 Exam Jam Problem Set MATH 154 Problem: 1 a) Find the radian and degree measures of the central angle θ subtended by the given arc of length s on a circle of radius r . b) Find the area of the sector determined by θ . s = 7cm, r = 4 cm Problem: 2 a) Find the angular speed (in the radians per minute) b) Find the linear speed of a point on the circumference (in ft/min) radius 5in., 40 rpm Problem: 3 Use fundamental identities to write the first expression in terms of the second, for any acute angle θ cot θ , sin θ Problem: 4 Verify the identity θ θ θ θ sin tan cos sec = - Mathematics Assistance Center, IUPUI Page 1 of 12
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Fall 2009 Exam Jam Problem Set MATH 154 Mathematics Assistance Center, IUPUI Page 2 of 12
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Fall 2009 Exam Jam Problem Set MATH 154 Problem: 5 Find the exact value a) csc ( 29 4 3 π b) csc ( 29 3 2 π - Problem: 6 Approximate, to the nearest 0.01 radian, all angles θ in the interval [ 29 π 2 , 0 that satisfy the equation a) θ sin = 0.4195 b) θ tan = -3.2504 c) θ sec = 1.7452 Problem: 7 Find the amplitude, the period, and the phase shift and sketch the graph ( 29 π - - = x y 3 sin 2 Problem: 8 An airplane takes off at a ° 10 angle and travels at the rate of 250ft/sec. Approximately how long does it take the airplane to reach an altitude of 15,000 feet. Mathematics Assistance Center, IUPUI Page 3 of 12
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Fall 2009 Exam Jam Problem Set MATH 154 Problem: 9 Verify the identity γ γ γ 2 csc 2 cos 1 1 cos 1 1 = + + - Problem: 10 Verify the identity k k k 2 4 4 sec 2 1 sec tan - = - Problem: 11 Find all solutions of the equations.
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