Gary Delia AMS151 Fall 2009 Homework Set 3 due 10/07/2010 at 11:59pm EDT 1. (2 pts) The angle of elevation to the top of a building is found to be 9 from the ground at a distance of 6000 feet from the base of the building. Find the height of the building. 950.306640843264 2. (2 pts) A plane is flying at an elevation of 33000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 21. Find the distance between the plane and the airport. Find the distance between a point on the ground directly below the plane and the airport. 92084.1277181031 85967.9392425102 3. (2 pts) For 0 < θ < /2, find the values of the trigonometric functions based on the given one (give your answers with THREE DECIMAL PLACES or as fractions, e.g. you can enter 3/5). If sec(θ) = 8 3 then csc(θ)= sin(θ) = cos(θ) = tan(θ) = cot(θ) = 1.07871977994119.927024810886958.375 2.47206616236522.404519917477945 4. (2 pts) For 0 < θ < /2, find the values of the trigonometric functions based on the given one (give your answers with THREE DECIMAL PLACES or as fractions, e.g. you can enter 3/5). If tan(θ) = 8 1 then cot(θ) = sin(θ) = cos(θ) = 1 sec(θ) = csc(θ) =.125.992277876713668.124034734589208 8.06225774829855 1.00778221853732 5. (2 pts) A hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 14 and 17. How high is the balloon? Give your answer in FEET not miles. NOTE: your angles must be entered in radians, even though the problem is posed in terms of degrees. BR 7135.82638595321 6. (2 pts) A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 30. From a point 1500 feet closer to the mountain along the plain, they find that the angle of elevation is 33. How high (in feet) is the mountain? NOTE: your angles must be entered in radians, even though the problem is posed in terms of degrees. BR 7804.9453036488 7. (2 pts) If θ = 1 6, then.499999999481858.866025404083588.577350268391894 1.15470053798039 8. (2 pts) Evaluate the following expressions. Your answer must be an angle /2 θ in radians. sin 1 ( 3 2 ) sin 1 ( 2 1) cos 1 ( 1 2 ) cos 1 ( 1)
1.0471975511966-0.523598775598299 1.0471975511966 3.14159265358979 9. (2 pts) If θ = 5 6, then.50000000259071-0.866025402288691-0.577350273178285-1.15470054037358 10. (2 pts) Evaluate the following expressions. Your answer must be an angle in radians and in the interval [ 2, 2 ]. (a) sin 1 ( 3 2 ) = (b) sin 1 ( 2 2 ) = (c) sin 1 ( 1) = -1.04719756666667-0.785398175-1.57079635 11. (2 pts) If sin(θ) = 24 25, 0 θ /2, then.28 3.42857142857143 3.57142857142857 12. (2 pts) For each of the following angles, find the degree measure of the angle with the given radian measure: 4 6 5 4 5 3 3 2 2 120 225 300 270 360 13. (2 pts) Evaluate the following expressions. sin(sin 1 ( 2 2 )) cos(cos 1 ( 2 1)) tan(tan 1 ( 1 2 )).707106781186548.5-0.5 14. (2 pts) If cos(θ) = 17 8, 0 θ /2, then.882352941176471 1.875 2.125 15. (2 pts) Evaluate the following expressions. cos(sin 1 ( 1 2 )) tan(sin 1 (0)).866025403784439 16. (2 pts) If tan(θ) = 15 8, 0 θ /2, then.882352941176471.470588235294118 2.125 17. (2 pts) For each of the following angles, find the radian measure of the angle with the given degree measure (you can enter as pi in your answers): 60 310 300 250 140 1.0472-5.41053333333333 5.236-4.36333333333333 2.44346666666667 2
18. (2 pts) Evaluate the following expressions. sin(cos 1 ( 1 2 )) tan(cos 1 ( 2 2 )).866025403784439 1 19. (2 pts) If sec(θ) = 13 5, 0 θ /2, then.923076923076923.384615384615385 2.4 20. (2 pts) For each of the followings angles (in radian measure), find the sin of the angle (your answer cannot contain trig functions, it must be an arithmetic expression or number): 6 4 3 2 2.5.707106781186548.866025403784439 1 23. (3 pts) If θ = 11 4, then Note:You can use sqrt() as sqare root..707106788167058-0.707106774206037-1.00000001974386 24. (3 pts) If θ = 1 3, then.86602540318614.500000001036284 1.73205080278249 25. (2 pts) A compact disk spins at a rate of 200 to 400 revolutions per minute.what are the equvilent rates measured in radians per second? to 20.943951 41.887902 21. (2 pts) Evaluate the following expressions. sin(tan 1 ( 3 3 )) cos(tan 1 ( 3)).5.5 22. (2 pts) Evaluate the following expressions. sin(cos 1 ( 4 5 )) tan(sin 1 ( 12 13 )).6 2.4 3 26. (2 pts)
Note: 2: The right side number on x-axis is 5 pi. 4: Clicking the graph will give you a bigger picture of it. 10*sin((2/5)*x) 28. (2 pts) Note: 2: The right side number on x-axis is 7 pi. 4/2*sin((2/7)*x)+4/2 27. (2 pts) Note: 2: The right side number on x-axis is 2 pi. -7*sin(1/(2/2)*x) 29. (2 pts) 4 Note:
2: The right side number on x-axis is 9 pi. -2*cos(1/(9/2)*x) 30. (2 pts) A population of animals oscillates sinusoidally between a low of 100 on January 1 and a high of 900 on July 1. Graph the population against time. Find a formula for the population P as a function of time, t, measured in months since the start of the year. P(t)= -(900-100)/2*cos(t/12*2*3.14159265)+(100+900)/2 31. (4 pts) The Bay of Calculus in Canada is reputed to have the largest tides in the world. The difference between low and high water levels is 300 feet. Suppose at midnight Jan,1, the depth of the water is 700 feet. High tide is at 6 am. Assume that the depth, y, of water as a function of time t (in hours) is given by y = D + Acos(B(t C)). What is the value of A? 33. (2 pts) Find the asymptotes for the following function. y = 9 20x 1x+12 vertical asymptote x= horizontal asymptote y= -12-20 34. (2 pts) Find the asymptotes for the following function. y = 9x2 +19x+1 12x 2 8 Vertical asymptotes: positive asymptote: x= negative asymptote: x= Horizontal asymptote y=.816496580927726-0.816496580927726.75 35. (2 pts) Which of the functions 1-3 meet each of the following descriptions? There may be more than one function for each description, or none at all. What is the value of B, assuming the time between successive high tides is 12 hours? What is the value of C? What is the value of D? 150.523598775 6 850 32. (3 pts) Graph each of the following polynomials on a graphing calculator or computer and use the graphs to determine if the function is odd, even, or neither. (use o as odd, e as even, n as neither). 1. g(x) = x 5 2x 3 2. e(x) = x 3 + 3x 2 3. i(x) = 7x + 5 4. f (x) = x 4 x 2 5. c(x) = x 4 o n n e e 5 1. y = x 1 x 2 +1 2. y = x2 1 x 2 +1 3. y = x2 +1 x 2 1 A. Horizontal asymptote of y=1 B. The x-axis is a horizontal asymptote C. Symmetric about the y-axis D. An odd function E. Vertical asymptote at x=1 and x=-1 b ac ace 36. (2 pts) The height of an object above the ground at time t is given by s = 6t 16t 2. At what height is the object initially? How long is the object in the air before it hits the ground? When will the object reach its maximum height? use a graphing calculator if you want.).375 (You can
.1875 37. (2 pts) Consider a box-shaped package with square ends.the US postal service will accept such a package if the sum of its length plus girth is less than 200 inches. (The girth is the perimeter of the square cross-section perpendicular to the length.) Find a formula for the volume,v,of a package which just meets the post office criteria in terms of s, the length of the side of the square end. V (s) = s**2*(200-4*s) 38. (2 pts) After running 14 miles at a speed of x mph, a man walked the next 4 miles at a speed that was 9 mph slower. Express the total time, T, spent on the trip as a function of x. What horizontal and vertical asymptotes does the graph of this function have? T (x)= Horizontal asymptote y= Vertical asymptote x= (for values of x greater than zero) 14/x+4/(x-9) 9 39. (2 pts) Are the funtions continuous on the given intervals?(using t as true,f as false) 1 1. on[3,4] (2x 5) 2. 1 sin(x) on[ /2,/2] 3. x x 2 +2 on[ 2,2] t f t 40. (2 pts) For what value of the constant c is the function f continuous on (, ) where { ca + 6 if a (,5] f (a) = ca 2 6 if a (5, ) c= NOTE: If your screen does not display the formula for function f (x), change the Display Mode at the bottom of the problem page to typeset..6 Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester 6