Take-Home Quiz # 4 (Sections 10.2 – 10.7) Math 115/6383, Due 11:59PM, Sunday February 23, 2020 Instructions: This quiz must be completed independently. You are allowed to consult with your notes or the textbook as needed to aid you in solving these problems. Seeking help from others in or out of the class is not allowed. Suggestions about how to approach this quiz: 1. Finish all homework assignments of the sections and get good understanding of the contents from the last week. 2. Print out a copy of the quiz and solve any problems that you can, using pencil and paper. 3. Review the eBook sections associated with any problems you could not solve. 4. Complete the remaining problems to the best of your ability. Even if you cannot come to a final solution, you should show what you do know so that you have the opportunity for partial credit. 5. Review your work. Check for errors. Make sure you have included units where appropriate, and explanations when required by the instructions. Unless the problem explicitly states otherwise, work must be shown for every answer. Any answer, even if “correct” but lacking work, will NOT receive full credit and may receive NO credit! 6. When you are satisfied, type in your solutions (extend space if needed) or, if you have the facilities, you can scan your hand written work or take photos with your camera. Make sure that your submission is readable and is a single document. 7. Submit your work in the associated LEO assignment. Unless the problem explicitly states otherwise, work must be shown for every answer. Any answer, even if “correct” but lacking work, will NOT receive full credit and may receive NO credit! Please submit the quiz as an attachment in any readable formats such as scanned or photo copy before or on Sunday, February 23. No late quiz will be accepted. No make-up quiz will be arranged. A solution key for Quiz # 4 will be posted after 12pm (EST), Monday, February 23. Please sign (or type) your name below the following honor pledge: I have completed this quiz by myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. Name ________________ _____ Date_____________________ QUIZ # 4 Problems 1. (6 pts) NOTE: For (b) and (c), your answers may involve square roots. Rationalize denominators where appropriate. (a) State the reference angle associated with 315. (b) State the exact value of sin(315). (c) State the exact value of tan(5π/3). 2. (6 pts) Using a calculator to help you find each of the following values, rounding the result to four decimal places. Be sure your calculator is in the proper angle measurement model! (a) sin(28.5) (b) sec(28.5) (c) cos(4π/7) For #3, you are welcome to use the following template if you like – just edit the labels (“___”) as desired. ___ ______ ______ ______ ____ 3. (9 pts) Given a right triangle having an acute angle  of 12and an adjacent side of length 21.0, 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 opposite to  and which is the length of the hypotenuse, as well as stating the measure of the other acute angle. Report the lengths rounded to one decimal place. 4. (12 pts) Suppose that the point (−7, 15 ) 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( ) = 5. (10 pts) A person is sitting on the ground between the Acme and Baker buildings. The person is 48 feet from the Acme building. The Baker building is 47.2 feet tall. From the person’s point of view, the angle of elevation to the top of the Acme building is 73 and the angle of elevation to the top of Baker building is 60. 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 47.2’ 73 60 48’ 6. (7 pts) Use a sum or a difference identity to find the exact value of sin (285). Show work. 7. (9 pts) Given that cos( ) = – 3/5 for an angle  in Quadrant II, find the exact values of each of the following. Show work. Rationalize denominators as appropriate. (a) sin( ) (b) cos(2 ) (c) sin(2 ) 2   8. (6 pts) Consider y = 9 sin  5t −  3   (a) State the amplitude. (b) State the period. (c) State the phase shift. (no explanation required) 9. (8 pts) State all of the exact solutions of the equation sin(2x) = 1/2 in the interval [0, 2). 10. (7 pts) Consider the following graph of a transformation of a trigonometric function. (no explanations required) (a) Is the function even, odd, or neither even nor odd? (b) State the period. (c) Which of the following functions corresponds to the graph? A. f (x) = cos(2x) – 3 B. f (x) = – sin(x) – 2 C. f (x) = sin(2x) – 2 D. f (x) = – cos(x) – 1 11. (10 pts) Prove the identity tan ( ) + cot ( ) = sec( )csc( ) . HINT: Rewrite each side of the expression using sines and cosines, simplify and apply a Pythagorean identity. Show work. 12. (10 pts) (a) Find the exact value of arcsec(2). (b)   2  . Find the exact value of tan  arccos   2    (c)  cos 4 Find the exact value of arccos  2 (d)  cot 3  Find the exact value of arcsin    3  (e) Using a calculator, find arccos(0.3814), rounded to four decimal places.  .  7.4.1 Exercises In Exercises 1 - 8, graph the ellipse. Find the center, the lines which contain the major and minor axes, the vertices, the endpoints of the minor axis, the foci and the eccentricity. 7. (SEE OTHER ATTACHMENT FOR PICTURE OF THE PROBLEM)
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