tm7 - MAC 1114 Module Test 7...

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Unformatted text preview: MAC 1114 Module Test 7 Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the following as an algebraic expression in u, u > 0. 1) sin arcsin u 3 A) u2 + 3 u2 + 3 B) u 3 C) u 3 Using a calculator, evaluate the expression. 2) sec (arctan 4.839) A) 4.9412 B) .2024 3 D) u u2 - 3 u2 - 3 C) .4999 D) 1.0000 C) 2.74126980 D) 2.82857139 C) 5π 6 D) 1π 4 C) θ = 7.93 ° D) θ = 82.07 ° Use a calculator to give the real number value. 3) y = cos-1(-.9397) A) 2.79254838 B) -.34920634 Find the exact value of the real number y. 4) y = arctan 3 3 A) π 3 B) π 6 Use a calculator to give the value in decimal degrees. 5) sec-1 7.246 A) θ = -7.86 ° B) θ = 7.86 ° Write the following as an algebraic expression in u, u > 0. 6) sin(arctan u) A) u u2 - 1 u2 - 1 B) u2 + 1 u2 + 1 C) u u2 + 1 D) u TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Provide an appropriate response. 7) True or False? To calculate inverse secant on a calculator use the fact that sec-1 x = 1 1 . cos-1 x u2 + 1 u2 + 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 8) The range r of a projectile is given by r = 1 v 2 sin 2θ, 32 where v is the initial velocity and θ is the angle of elevation. If r is to be 2000 ft and v = 4500 ft/sec, what must the angle of elevation be? Give your answer in degrees to the nearest hundredth. A) 0.18 ° B) 89.91 ° C) 0.09 ° D) 0.13 ° Solve the equation exactly over the interval [0, 2π). 9) 2 sin 2x = sin x A) π , 2π 33 B) 0, π, π , 5π 66 C) π , 3π , π , 2π 2233 D) π , 5π 66 C) 3π , 5π 4 4 10) cos x = sin x A) π , 7π 44 B) 3π , 7π 4 2 Solve the equation exactly over the interval [0,360 °). 11) (tan θ + 1)(2 cos θ - 1) = 0 A) {0°, 135°, 225°} C) {45°, 60°, 225°, 240 °} D) π , 5π 44 D) π 2 B) {30°, 135°, 150°, 315°} D) {60°, 135°, 300°, 315°} Solve the equation exactly over the interval [0, 2π). 12) sin x + 4 = 3 A) π , 2π B) 3π 33 2 C) {0, π} Solve the problem. 13) It can be shown that if the angle of elevation from an observer to the top of an object is A and the angle of elevation d ft closer is B, then the height of the object is given by d h= ft. cot A - cot B Find A if h = 30 ft, d = 80 ft, and B = 56°. Give your answer in degrees to the nearest hundredth. A) 21.76 ° B) 16.66 ° C) 26.51 ° D) 11.28° Solve the equation exactly over the interval [0, 2π). 14) tan 2x - tan x = 0 A) π , 5π 44 B) C) {0, π} π , π , 2π , 7π , 7π , 13π , 5π 12 6 3 12 6 12 3 D) {0} 2 Solve. 15) The weekly sales in thousands of items of a product has a seasonal sales record approximated by n = 66.83 + 26 sin πt 24 (t = time in weeks with t=1 referring to the first week in the year). During which week(s) will the sales equal 79,830 items? A) week 21 and week 30 B) week 4 and week 47 C) week 4, week 20, and week 52 D) week 30 and week 47 Solve the equation exactly over the interval [0, 2π). 16) 2 3 sin 4x = 3 A) π , π , 2π , 7π , 7π , 13π , 5π , 19π 12 6 3 12 6 12 3 12 C) B) {0} π , 5π 44 D) 0, π , π 4 Solve. 17) In an electrical circuit, let V represent the electromagnetic force in volts at t seconds. Assume V = cos 2πt. Find the smallest positive value of t where 0 ≤ t ≤ 1 for V = 2 A) 1 sec 12 B) 1 sec 2 3. C) 1 sec 6 Solve the equation exactly over the interval [0, 2π). 18) cos 2x = 2 - cos 2x A) 0, 2π , π, 4π 3 3 C) 2 B) ∅ π , 3π , 5π , 7π 44 4 4 D) Solve the equation exactly over the interval [0,360 °). 19) sin 2θ = cos θ A) {30°, 90°, 150°, 270°} C) {105°, 165°, 285°, 345°} π , 9π , 7π , 15π 88 8 8 B) {0°, 120°, 180°, 240°} D) {15°, 165°, 195°, 345°} Solve the equation exactly over the interval [0, 2π). 20) sin 2x + sin x = 0 B) , 2π , π, 4π 3 3 A) ∅ C) π , 3π , 5π , 7π 44 4 4 D) 3 π , 9π 88 D) 0 sec ...
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This note was uploaded on 10/18/2011 for the course MAC 1114 taught by Professor Russel during the Summer '08 term at Valencia.

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