MATH 115 QUIZ 4 NAME: _______________________________ May-July, 2016 Instructor: B. Stec I have completed this assignment myself, working independently and not consulting anyone except the instructor. INSTRUCTIONS The quiz is worth 100 points. There are 10 problems. This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than Sunday, June 26. Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work. General quiz tips and instructions for submitting work are posted in the Quizzes module. If you have any questions, please contact me by e-mail. 1. (10 pts) NOTE: Compute values analytically (by \"hand\") if possible, for remaining problems use calculator. (a) and (b), may involve square roots so use them in your answers. (a) State the exact value of sin(120). (b) State the exact value of tan(2/3). (c) cos(83) (d) sec(83) (d) sin(5/8) 2. (10 pts) Given a right triangle having an acute angle of 15and hypotenuse of length 5.0, find the measurement of the other angle and the other sides. Show work. Be sure to clearly identify which of your answers is the length of the side adjacent to and which is the length of the side opposite , as well as stating the measure of the other acute angle. Report the lengths rounded to one decimal place. For #2, you are welcome to use the following template if you like - just edit the labels (\"___\") as desired. ______ ________ ________ ______ ________ 3. (10 pts) Suppose that the point (7, 3) lies on the terminal side of an angle in standard position. Find the exact values of the six trigonometric functions of . Work optional. Rationalize denominators as appropriate. sin( ) = cos( ) = tan( ) = csc( ) = sec( ) = cot( ) = 4. (12 pts) A person is sitting on the ground between the Acme and Baker buildings. The person is 34 feet from the Acme building. The Baker building is 58.2 feet tall. From the person's point of view, the angle of elevation to the top of the Acme building is 63 and the angle of elevation to the top of Baker building is 45. Show work in answering the following questions: (a) How tall is the Acme building? (b) How far apart are the two buildings? Report the values to the nearest tenth of a foot. Acme Baker 56' 62.4 45 34' 5. (8 pts) Use a sum or a difference identity to find the exact value of cos(105). Show work. 6. (12 pts) Given that sin( ) = 4/7 for an angle in Quadrant II, find the exact values of each of the following. Show work. Rationalize denominators as appropriate. (a) cos( ) (b) sin(2 ) (c) cos(2 ) 7. (8 pts) Consider = 3 (5 ) 2 (a) State the amplitude. (b) State the period. (c) State the phase shift. (no explanation required) 8. (9 pts) State all of the exact solutions of the equation sin(2x) = 1/2 in the interval [0, 2). (work optional) 9. (9 pts) Prove the identity sec cos tan sin . HINT: Rewrite each side of the expression using sines and cosines, simplify and apply a Pythagorean identity. Show work. 10. (12 pts) (work optional) (a) Find the exact value of arcsec(2). 3 (b) Find the exact value of tan (arcsin ( 2 )). (c) Find the exact value of arcsin (sin (d) Find the exact value of arccos (tan 3 2 ). 5 4 )