MATH 114 FALL 2014 EXAM #1 SAMPLE

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Reynard Howard
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1 DO NOT BEGIN THIS TEST UNTIL YOU ARE TOLD TO DO SO. You will have 50 minutes from this time to finish the test. 1) You will need a pencil or pen, one calculator and this exam paper. Please clear everything else from your desk. (Please turn off or switch cell phones to manner mode.) 2) Calculators such as the TI86, TI89, TI-NSPIRE, Voyage 200, TI92, TI92+, HP49G, HP49G+, HP50G, Casio algefx2.0, algefx2.0pls or laptop, handheld, desktop and palmtop computers are NOT to be used. The use of cell phones, PDAs, Blackberries, head sets, or any other wireless device in the classroom is specifically prohibited. Please do not ask your recitations TAs/proctors about calculator use or mode. You must clear all programs from your calculator memory. 3) Please look at overhead for possible corrections to this exam. 4) Do not spend too much time on a particular problem. Work the problems that are simplest for you first. 5) On the open-ended questions, the grading will be based on your method. Show all of your work. NO WORK = NO CREDIT! You must show work that supports your answer in order to get credit. Be neat and orderly. If you need additional space, use the back of the exam pages. 6) For open-ended questions, show your work and place your answers on the lines or in the boxes provided. Answers can be in any form unless otherwise specified. For problems asking for EXACT answers, leave in terms of fractions, and number. For decimal answers, round to 4 decimal places unless otherwise specified. You must simplify your solutions. You should have no complex fractions. 7) Give measurement units (feet, degrees, etc.) when appropriate. 8) This exam consists of 12 problems on 7 pages including this cover page. 1

2 1. (16 points) FILL IN the entire UNIT CIRCLE indicating angles (in EXACT radian measure in terms of π) with their corresponding EXACT (x, y) coordinates: 2

3 3. (6 points) QUADRANT LOCATION. Use the given criteria to identify and CIRCLE the correct quadrant location. (2 points each. No work required. No partial credit.) i Given tan 0 and sin 0, the terminal side of angle θ is in quadrant: a. QI b. QII c. QIII d. QIV e. No quadrant ii The terminal side of an angle in standard position measuring 265 is in quadrant: a. QI b. QII c. QIII d. QIV e. No quadrant iii. The terminal side of an angle in standard position measuring 4.8 is in quadrant: a. QI b. QII c. QIII d. QIV e. No quadrant 3. (12 points) Determine the EXACT VALUES of the following trigonometric functions. Show all work including trig identities used. No complex fractions allowed as solutions. You do not need to rationalize. (4 points each.) i. 11 cos 4 ii. 2 csc 3 iii. 11 tan 6 3

4 4. (9 points) Given the following right triangle, find the EXACT VALUE of each. Show all work including trig definitions in general. Simplify radicals and reduce fractions. You do not need to rationalize θ a) sec b) tan 2 5. (12 points) TRUE or FALSE. For each statement, CIRCLE TRUE or FALSE. (2 points each. No work required. No partial credit.) i. An angle is in standard position when the vertex is at the origin of TRUE FALSE a coordinate system and the initial side is on the positive x-axis. ii is in decimal notation.. TRUE FALSE iii. sin cos 1 is an identity. TRUE FALSE iv. Supplementary angles are positive angles that sum to 90º or 2. TRUE FALSE v. One radian has approximately the same measure as one degree. TRUE FALSE 4

5 vi. The point 7 24, is on the unit circle. TRUE FALSE 6. (6 points) An airplane is descending from a height of Y feet to its specified runway at an angle of depression of 56º. What is the airplane s initial height Y given the diagonal distance to the runway is 41,000 feet? Draw a fully labeled illustration, clearly identifying the angle of depression, as part of your solution. Show all mathematical work. Provide at least ± 0.01 decimal place accuracy. 7. (12 points) Find the EXACT VALUES of the following trigonometric functions of 101 given sec csc 0 99 and. [Show all work including REFERENCE TRIANGLE and/or basic trigonometric identities and definitions in general (before putting in numerical values)] a) tan a) b) cos 5

6 b) 8. (7 points) Given the radius of the earth is approximately 3960 miles, find the distance between Lansing, MI with latitude 42.7 North and Lexington, KY with latitude 38 North. Show all mathematical work. Provide at least ± 0.01 decimal place accuracy. 9. (8 points) Use trigonometric identities and the Complementary Angle Theorem to find the EXACT VALUE of the expression. [Show ALL intermediate steps. There are at least 6 changes. No work = No credit. No decimal approximations allowed in work or solution.] 2 2 sec 36 sin 36 sin 54 cot 36 tan 36 csc

7 # (12points) SHORT ANSWER. Show all work. (4 points each.) 10. The point 8,15 is on the terminal side of an angle θ in standard position. Find the EXACT VALUE of sin. Simplify any radical. 11. Find the reference angle β' for β = 263 in standard position Find a negative coterminal angle for in EXACT radian measure. 8 7

Math 114 PRACTICE EXAM 3

Math 114 PRACTICE EXAM 3 Math 114 PRACTICE EXAM DO NOT BEGIN THIS TEST UNTIL YOU ARE TOLD TO DO SO. You will have 50 minutes from this time to finish this exam. 1) This exam consists of 1 questions on pages including this front