Math 150 Test 1 Study Guide
Order ID 53563633773 Type Essay Writer Level Masters Style APA Sources/References 4 Perfect Number of Pages to Order 5-10 Pages Description/Paper Instructions
Math 150 Test 1 Study Guide
Math 150 Test 1 – Study Guide (Chapter 1 – 4) 1) Evaluate: sin2 124° + cos2 124° 2) Evaluate: sec2 53° – tan2 53° 3) Determine whether each statement is possible or impossible: cos 𝜃𝜃 = − 54.3 4) Convert 105∘20′32′′ to decimal degrees to the nearest thousandth.
5) Convert −19.361∘ to degrees, minutes, and seconds to the nearest second. 6) A circle has radius 15.6 cm. Find the length of the arc intercepted by a central angle of 132∘.
Answer must include UNITS. 7) Find the area of a sector of a circle having radius 𝑟𝑟 = 17.2 ft and central angle 𝜃𝜃 = 185∘.
Answer must include UNITS.
8) Given latitudes of Los Angeles, 34°N, and Reno, 40°N. Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Use 𝑟𝑟=6400 km for the radius of Earth.
Answer must include UNITS. 9) Find the linear speed 𝑣𝑣 of the tip of the hour hand of a clock if the hand is 15 cm long.
Answer must include UNITS.
10) Find the linear speed 𝑣𝑣 of a point on the tread of a tire of radius 18 cm, rotating 35 times per min.
11) Assume 𝐶𝐶 = 90∘. Solve right triangle 𝐴𝐴𝐴𝐴𝐶𝐶, if 𝑏𝑏 = 35.6 ft and 𝑐𝑐 = 61.7 ft. 12) Solve the right triangle ABC with 𝑐𝑐 = 12.7 𝑖𝑖𝑖𝑖, 𝐴𝐴 = 34°30′. Assume C is the right angle. 13) Radar stations 𝐴𝐴 and 𝐴𝐴 are on an east-west line, 5.7 km apart. Station 𝐴𝐴 detects a plane at 𝐶𝐶, on a bearing
of 42∘. Station 𝐴𝐴 simultaneously detects the same plane, on a bearing of 312∘. Find the distance from 𝐴𝐴 to 𝐶𝐶. Answer must include UNITS.
14) A ship leaves port and sails on a bearing of N 47° E for 3.5 hours. It then turns and sails on a bearing of S 43° E for 4 hours. If the ship’s rate is 22 knots (nautical miles per hour), find the distance that the ship is from the port. Round to the nearest whole number. 15) The angle of depression from the top of a building to a point on the ground is 67∘. How far is the point on the ground from the top of the building if the building is 194 m high? Answer must include UNITS. 16) From a window 62.0 ft above the street, the angle of elevation to the top of the building across the street is 56.0∘ and the angle of depression to the base of this building is 13.0∘. Find the height of the building across the street. Answer must include UNITS. 17) You need to find the height of a building. From a given point on the ground, you find that the angle of
elevation to the top of the building is 74.2∘. You then walk back 35 ft. From the second point, the angle of elevation to the top of the building is 51.8∘. Find the height of the building. Answer must include UNITS.
18) Graph 𝑦𝑦 = 4sin(𝑥𝑥 − 𝜋𝜋) + 3 over a two-period interval. Label 5 key points in one period based on the question.
19) Graph 𝑦𝑦 = −5cos(4𝑥𝑥 + 2𝜋𝜋) over a two-period interval. Label 5 key points in one period based on the question.
20) Graph 𝑦𝑦 = −3 csc �𝑥𝑥
2 �. Label vertical asymptotes and 2 key points in the period based on the question.
21) Graph 𝑦𝑦 = 2 sec �𝑥𝑥
6 �. Label vertical asymptotes and 2 key points in the period based on the question.
22) Graph 𝑦𝑦 = −2 cot �2𝑥𝑥 + 𝜋𝜋
4 � Label vertical asymptotes and 3 key points in the period based on the
question.
23) Graph 𝑦𝑦 = 3 tan(3𝑥𝑥 − 𝜋𝜋) Label vertical asymptotes and 3 key points in the period based on the question.
24) Identify the quadrant (or possible quadrants) an angle 𝜃𝜃 that satisfies the given conditions:
tan 𝜃𝜃 < 0 , csc 𝜃𝜃 > 0
25) Find the measure of the supplementary angle of 42°. 26) Use a calculator to find a decimal approximation to five decimal places for cos 74∘35′. 27) Find the value t to four decimal places in the interval �0, 𝜋𝜋
2 � if sec 𝑡𝑡 = 5.0447
28) Convert 23𝜋𝜋 15
to degrees. 29) Convert 105° to radians. 30) Find the exact value of sin 30° − cot 45°. 31) The terminal side of an angle 𝜃𝜃 in standard position passes through the point �−2, −√5�.
Find the exact values of sec 𝜃𝜃. (No decimal answer allowed.) 32) Find the exact values of sin 𝜃𝜃, given that tan 𝜃𝜃 = 7
24 and 𝜃𝜃 is in quadrant III. (No decimal answer allowed.)
33) Find one solution to the following equation.
cot(25° − 3𝜃𝜃) = tan(5𝜃𝜃 + 13∘)
34) Find the reference angle for 562∘ 35) Find the reference angle for − 41𝜋𝜋
3
36) Find the exact value for sec (−180∘). (No decimal answer allowed.)
37) Find the exact value for cot 3𝜋𝜋
2 . (No decimal answer allowed.)
38) Find the exact value for cos(480∘) . (No decimal answer allowed.)
Must show the reference angle on the x-y plane with the correct labelling on all 3 sides of the reference triangle to receive credit.
39) Find the exact value for csc 13𝜋𝜋
6 . (No decimal answer allowed.)
Must show the reference angle on the x-y plane with the correct labelling on all 3 sides of the reference triangle to receive credit.
40) Find the exact value for tan �− 17𝜋𝜋 4 �. (No decimal answer allowed.)
Must show the reference angle on the x-y plane with the correct labelling on all 3 sides of the reference triangle to receive credit.
RUBRIC
QUALITY OF RESPONSE NO RESPONSE POOR / UNSATISFACTORY SATISFACTORY GOOD EXCELLENT Content (worth a maximum of 50% of the total points) Zero points: Student failed to submit the final paper. 20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. 30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking. 40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete. 50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing. Use of Sources (worth a maximum of 20% of the total points). Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper. 5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. 10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. 15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. APA 6th Edition is used with only a few minor errors. There are minor errors in reference and/or citations. And/or there is some use of questionable sources. 20 points: Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented. APA 6th Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment. 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