Name _____________________________________________ ID Number _______________________ Unit 7 Evaluation Advanced Algebra 2 (MTHH 040 057) This evaluation will cover the lessons in this unit. It is open book, meaning you can use your textbook, syllabus, and other course materials. To submit the evaluation, follow the directions provided. A graphing calculator may be used on this evaluation. You may also use scratch paper to work out the solutions. Select the response that best completes the statement or answers the question. ____1. Which expression is not equal to the other three expressions? a. b. c. d. 2 tan cot  1 2 sin  1 cos  2 2cos  sin  ____2. Which equation is not true? a. cos2   1  sin2  b. cot2   csc2   1 c. sin2   cos2   1 d. tan2   sec2   1 ____3. Which expressions are equivalent? I. (sin )(csc   sin ) II. sin2   1 III. cos2  a. I and II b. II and III Unit 7 Evaluation MTHH 040 c. I and III d. I, II, and III ____4. How can you express csc2   2cot2  in terms of sin  and cos ? a. b. 1  2 cos 2  sin2  1  2 sin2  sin2  c. sin2   2cos2  1 2 d.  2 sin  tan2  ____5. Which expression is equivalent to tan  ? cos   sec  a. csc  b. sec  c.  csc  d. tan2  ____6. Which of the following is not equal to 60 ? 3 2 1 b. cos1 2 1 3 c. tan a. sin1 d. tan1 3 3 ____7. In which quadrants would you find the solutions to tan   1  0 ? a. Q1 & QII b. QII & QIII c. QII & QIV d. QIII & QIV ____8. Which of these angles have a sine of about –0.6? I. 143.1 II. 216.9 III. 323.1 a. I and II b. I and III c. II and III d. I, II, and III Unit 7 Evaluation MTHH 040 ____9. What are the solutions of 2sin   3  0 for 0    2 ?  5 and 6 6  2 b. and 3 3 2 4 c. and 3 3 4 5 d. and 3 3 a. ____10. Suppose a > 0. Under what conditions for a and b will a sin   b have exactly two solutions in the interval 0    2 ? a. a = b b. b > a c. a = –b d. a > b > –a ____11. A ladder rests against a vertical building. The ladder is 14 ft long and forms an angle of 76.5 with the ground. Which statement is not true? a. The bottom of the ladder is 13.6 ft from the base of the building. b. The bottom of the ladder is 3.3 ft from the base of the building. c. The top of the ladder is 13.6 ft from the ground. d. The ladder forms an angle of 13.5 with the building. ____12. The sides of a rectangle are 25 cm and 8 cm. What is the measure of the angle formed by the short side and a diagonal of the rectangle? a. b. c. d. 17.7 18.7 71.3 72.3 ____13. This figure is a rectangle. What is the value of x? a. 31.0 b. 36.9 c. 53.1 d. 59.0 ____14. In XYZ, Z is a right angle and tan X  8 . What is 15 sinY ? a. 8 17 Unit 7 Evaluation MTHH 040 15 17 17 c. 15 15 d. 8 b. ____15. In this right triangle, cos y  5 . If x + 2z = 13 7.1, what is the value of z? a. 67.3 b. 22.6 c. –7.75 d. –30.0 ____16. In a. b. c. d. GDL, mD  57, DL  10.1, and GL  9.4 . What is the best estimate for mG ? 64 51 39 26 ____17. Using which set of given information can you compute the area of an oblique triangle by applying the Law of Sines? a. Given: the length of one side and the measure of the angle opposite it. b. Given: the length of one side and the measure of the angle adjacent to it. c. Given: the lengths of two sides and the measure of a nonincluded angle. d. Given: the lengths of two sides and the measure of the included angle. ____18. A surveyor picks two points 250 m apart in front of a tall building. The angle of elevation from one point is 37 . The angle of elevation from the other point is 13 . What is the best estimate for the height of the building? a. 150 m b. 138 m c. 83 m d. 56 m Use the following diagram to answer questions 19–24. Angle measures are in degrees. Unit 7 Evaluation MTHH 040 ____19. Let a = 23.2, b = 18.5, and mC  42 . What is the value of c? a. 23.1 b. 12.4 c. 15.6 d. 8.7 ____20. Let a = 23.2, b = 18.5, and mC  42 . What is the value of mA ? a. 76.5 b. 23.2 c. 85.4 d. 42.3 ____21. Suppose a = 45.25, b = 39.75, and c = 20.65. What is mB ? a. 61.4 b. 54.4 c. 11.5 d. 89.7 ____22. Suppose a = 45.25, b = 39.75, and c = 20.65. What is mC ? a. 27.1 b. 16.5 c. 45.6 d. 36.9 ____23. Suppose b = 11.0, c = 11.7, and mA  22 . What is the length of the altitude from A? a. 11.7 b. 11 c. 13.4 d. 9.8 ____24. Suppose b = 11.0, c = 11.7, and mA  22 . What is the area of Unit 7 Evaluation ABC ? MTHH 040 a. 56.4 b. 24.2 c. 32.6 d. 18.8 ____25. Which expressions are equivalent? I. cos  II. cos( ) III. sin( ) tan( ) a. I and II b. II and III c. I and III d. I, II, and III ____26. Which expressions are equivalent?   I.  tan     2    II. tan     2         2 III. tan    a. I and II b. II and III c. I and III d. I, II, and III ____27. Which expression is equal to cos 50 ? a. b. c. d. sin 20 cos 30  cos 20 sin30 sin 20 cos 30  cos 20 sin30 cos 20 cos 30  sin 20 sin30 cos 20 cos 30  sin 20 sin30 ____28. Which expression is not equivalent to cos  ? a. b. c. d.  sin(  90)  cos( ) sin(  90)  cos(  180) ____29. Which expression is an exact value for sin15 ? 2 3 2   2 2 2 2 3 2   b. 2 2 2 2 1 2    c. 2 2 2 2 1 2    d. 2 2 2 a. 1 2 1  2 3 2 3 2  ____30. If  is in Q1 and sin   Unit 7 Evaluation 3 , what is an exact value of sin 2 ? 5 MTHH 040 9 25 24 b. 25 6 c. 5 a. d. 73.7 For questions 31–35, choose the correct term that completes each sentence. Some terms may be used more than once. a. Law of Cosines b. Law of Sines c. trigonometric identity d. trigonometric ratios for a right triangle _____ 31. You can find missing measures of any triangle by using the ______________ if you know the measures of two angles and a side. _____ 32. The six ratios of the lengths of the sides of a right triangle are known as the _______________. _____ 33. If you know the measures of two sides and the angle between them, you can use the ________________ to find the missing parts of any triangle. _____ 34. A trigonometric equation that is true for all values except those for which the expressions on either side of the equal sign are undefined is a _______________. _____ 35. The _____________ can be used to find missing measures of any triangle when you know two sides and the angle opposite one of them. Carefully check your answers on this evaluation and make any corrections you feel are necessary. When you are satisfied that you have answered the questions to the best of your ability, transfer your answers to an answer sheet. Please refer to the information sheet that came with your course materials. Unit 7 Evaluation MTHH 040 Blank page 
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