Page 1 of 7 1. Use a calculator to find tan   . Round the answer to 4 decimal places. 1. _______ A. −0.0990 B. −0.7265 C. 0.0990 D. 0.7265 2. For the triangle ABC, the following information is provided. C = 48°, a = 9, and b = 21. (Angle A is opposite side a, Angle B is opposite side b, Angle C is opposite side c.) State which case applies when solving the triangle and which law to use. 2. _______ A. Angle-Side-Side; law of cosines B. Angle-Side-Side; law of sines C. Side-Angle-Side; law of cosines D. Side-Angle-Side; law of sines 3. Identify the type of conic section represented by the equation 9x 2 + 4y 2 – 18x – 7 = 0. 3. _______ A. ellipse B. circle C. parabola D. hyperbola MATH 108 Trigonometry and Analytical Geometry Summer, 2017, 2.1 Page 2 of 7 4. Which of the functions corresponds to the graph? 4. ______ A. f (x) = 2(1 – cos x) B. f (x) = 2 + cos x C. f (x) = 2 – sin x D. f (x) = 3 – cos x 5. The matrix below is an augmented matrix for a system of three linear equations. What can be concluded about the solution of the system? 5. _______           − − 0 0 0 0 0 1 0 5 1 0 2 3 A. There are infinitely many solutions. The solutions are (−3 − 2t, 5, t) for all real numbers t. B. There are infinitely many solutions. The solutions are (−3 + 2t , 5, t) for all real numbers t. C. The system is inconsistent; there is no solution. D. The unique solution of the system is (2, −3, 5). MATH 108 Trigonometry and Analytical Geometry Summer, 2017, 2.1 Page 3 of 7 6. Which of the equations corresponds to the graph? 6. ______ A. r = 1 + cosθ B. r = 1 – cosθ C. r = 1 – 2 cosθ D. r = 1 + 2 sinθ 7. Consider the sequence 5, 12, 19, 26, 33, ... Is the sequence arithmetic or geometric, and what is the 26th term? 7. _______ A. geometric sequence; 187 B. geometric sequence; 180 C. arithmetic sequence; 187 D. arithmetic sequence; 180 8. Is the following the sum of an arithmetic sequence, a geometric sequence, or neither, and what is the sum?  5 2      8. _______ A. sum of arithmetic sequence; sum = 63.4375 B. sum of geometric sequence; sum = 39.0625 C. sum of geometric sequence; sum = 63.4375 D. sum of sequence which is neither arithmetic nor geometric; sum = 41.5625 MATH 108 Trigonometry and Analytical Geometry Summer, 2017, 2.1 Page 4 of 7 SHORT ANSWER: 9. (a) Give an example of an angle which is coterminal with 530°. Answer: ________ (b) Convert the angle   from radian measure into degree measure. Answer: ________ 10. Find the exact values (no decimal approximations). (a) sec 420° Answer: ________ (b) tan (−210°) Answer: ________ 11. Given y = 5 sin(8x – π), state the (a) period Answer: ________ (b) phase shift Answer: ________ 12. Solve the trigonometric equation (sin x)(2cos x + 1) = 0 = 0 in the interval [0, 360°). Find the exact values. Answer: _________________ 13. (a) Find the exact value of arcsin sin    Answer: ________ (b) Find the exact value of arccos tan   Answer: ________ MATH 108 Trigonometry and Analytical Geometry Summer, 2017, 2.1 Page 5 of 7 14. (a) Given the point (6, 150°) in polar coordinates, find a corresponding point in rectangular coordinates. (State exact values, not decimal approximations.) Answer: _________________ (b) Given the point (2, – 2) in rectangular coordinates, find a corresponding point in polar coordinates. Express the angle exactly in radians. (Your angle should include π). Answer: ________________ 15. For the parabola given by (y – 4)2 = 8(x + 6), find the following: (a) direction parabola opens (to the left, right, up, or down) Answer: ___________ (b) vertex Answer: ___________ (c) focus Answer: ___________ 16. Tickets at an amusement park cost $40 for adults and $32 for children. 1,500 tickets were sold, totaling $53,440 in receipts. Suppose you want to find out how many of each type of ticket were sold. Let x = number of adult tickets sold and y = number of children’s tickets sold. (a) Write a system of two equations involving variables x and y, corresponding to the information given about the tickets. Equation: ___________________________ Equation: ___________________________ (b) Find the solution of your system of equations from part (a). Solution: _________________ (c) Interpret the solution in a sentence, in terms of ticket sales at the amusement park. Sentence: _____________________________________________________________ _________________________________________________________________________ MATH 108 Trigonometry and Analytical Geometry Summer, 2017, 2.1 Page 6 of 7 SHORT ANSWER, with work required to be shown, as indicated. 17. A building contractor is planning to use a ladder to reach a window. If a 12-ft ladder leans against the building, with an angle of elevation of 70°, how far up the building will the ladder reach? Will the contractor be able to reach a window 10 feet above ground level? Show work. (sketch is not to scale) 18 . An ellipse has the equation (  ) + ("  )  = 1 (a) Is the major axis horizontal or vertical? (b) Find the exact values of the foci of the ellipse. Show work. 19. Suppose that sin θ = 12/13 and that θ is a Quadrant II angle. (a) Find the exact value of cosθ. Show work. (b) Find the exact value of sin (2θ ). Show work. 20. Prove the identity (cos x – sin x) 2 + sin(2x) = 1 70o 12ft ladder MATH 108 Trigonometry and Analytical Geometry Summer, 2017, 2.1 Page 7 of 7 21. For the triangle ABC, we are given that A = 46°, B = 64°, and c = 35.0. Find the length of side b, rounded to the nearest hundredth. Show work. 22. Let %&' = 〈6, –3〉 and (&' = 〈4, 8〉. (a) Calculate %&' + )(&'. Show work. (b) Calculate the exact length, or magnitude, of (&'. Show work. (c) Calculate the dot product %&' ∙ (&'. Show work. (d) Determine the angle between %&' and (&'. Round the result to the nearest degree. Show work. 23. Solve the system of equations, using Gaussian elimination with or without matrices, or Gauss-Jordan elimination (your choice of method) Show work. x – 2y + z = 3 2x + y + 2z = 11 –2x + y + z = 0 

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