This Math 114 final exam was administered in the Fall of 008. This is a sample final exam. The problems are not exhaustive. Be prepared for ALL CONCEPTS for the actual final exam. Multiple Choice Questions Circle the letter of the correct answer. 7 points each. 6 1. The exact value of tan a) 0 b) is: c) 1 d) e) 0.5775069 f) 1.7050808. The exact value of sin 1 1 is: a) b) c) 6 d) 5 6 e) 5 f) 11 6. For y = 4tan x, two consecutive vertical asymptotes are: a) x = 0, x = b) x =, x c) x =, x = d) x =, x = e) x = 7, x = 6 6 f) None of these. 4. The rectangular coordinates, converted to polar coordinates are: a), 4 b), 4 c), 4 5 d), 4 7 e), 4 f) None of these. 1
5. The exact value of csc 7 a) b) c) is: d) e) f) 6. A medical helicopter is 10 miles due south and 15 miles due east of a hospital. If the pilot wants to travel directly to the hospital, what bearing should be taken? a) S1.45 E b) S7.1 E c) N1.45 W d) N7.1 W e) N81 W f) N8.87 W g) N88.55 W h) N89.86 W 7. For an object in simple harmonic motion given by the model d 5 sin( 4t) where d is in feet and t is in seconds, the maximum displacement (in feet) and the frequency (in oscillations per second) of the object are (respectively): a) 5, 1 d) 5, 1 b) 5, c) 5, 4 e) 5, f) 5, 4 8. Find the exact value of the arclength of a circle with central angle 100 and diameter 4 feet: 18 a) feet 5 0 d) feet 9 10 b) feet c) feet 9 e) 00 feet f) 400 feet 9. The polar equation 4 r in rectangular form is: sec a) r = 4x b) r = 4y c) r 4 x d) r 4 y e) x y 4 x f) x y 4 y g) x y 16 x
Open-ended Questions Points for each question are labeled. Show ALL of your work. Give EXACT answers when requested. 10. (16 points) Given: a =. inches = 4 = 6 (a) Solve the triangle. Provide ±0.01 decimal place accuracy on solution. (b) Find the area of the triangle.
11. (18 points) For the given graph, write the function f ( x) A sin x B and find the following: [ x-scale and y-scale is 1.] 9 1 A = B = = = Amplitude Period Phase Shift Range (in interval notation) Function f ( x) = 4
1. (1 points) Verify the trigonometric identity. Show every step. Work going DOWN. Work on ONE side only: tan csc x x csc x cos( x) 5
1. (8 points) PLOT and label the following polar coordinates. CONVERT the point from polar to EXACT rectangular coordinates. 1 POLAR TO RECTANGULAR 5,, 14. (1 points) Find the EXACT value. Show all work including reference triangle. csc tan 1 1 0 6
15. (10 points) Find all solutions for in 0,. Give exact solutions, where possible. Otherwise, provide ±0.0001 decimal place accuracy. csc 7 cot 9 0 16. (10 points) Find all GENERAL solutions for θ in radian measure. Give EXACT algebraic solutions only. cos (sin 5 1) 0 7
17. (18 points) Given: sec α = 17 and 0 8 sin tan 15 and Find the EXACT value of: [Show all work and reference triangles.] a) sin b) cos 8
18. (15 points) A ship travels 58 miles due east then adjusts its course to N7 E. After traveling 89 miles in this direction, how far is the ship from its point of departure? [Include a labeled illustration as part of your solution, showing given bearing.] Solution should have ± 0.01 decimal place accuracy.] 9
19. (18 points) A woman entering an outside glass elevator on the ground floor of a hotel glances up to the top of the building across the street and notices the angle of elevation is 48. She rides the elevator up three floors (60 feet) and finds the angle of elevation to the top of the building across the street is. How tall is the building across the street? [Include a labeled illustration. Solution should have ± 0.01 decimal place accuracy.] 10
Math 114 Final Exam Monday, December 8, 008 Section # Name PID # FORMULA SHEET (Sum, Difference, Double and Half Angle Formulas Only) cos cos cos sin sin sin sin cos cos sin cos 1 cos tan tan tan 1 tan tan sin 1 cos sin cos sin cos cos sin tan = 1 cos sin = sin 1 cos 1 sin tan cos 1 tan 1 tan 11