# Progress Test 3

Course Name: Second Year Algebra 2 Course ID: MTHH040059 Student: Cole Dearmin Student ID: D48021432 Generated Date: May 31, 2021 Progress Test 3 Although the progress test is similar in style to the unit evaluations, the progress test is a closed-book test. It is important that you do your own work. Select the response that best completes the statement or answers the question. Your graphing calculator may be used on this progress test. You may also use scratch paper to work out the solutions. Use this link to access supplemental information that you may use as you take this Progress Test. ____ 1. How many cycles does the sine function, y = 3 sin θ, have in the interval from 0 to 2 ? A. 1 B. 2 C. 3 D. 4 ____ 2. Find the measure of the angle in standard position. A. 115° B. −155° C. 245° D. −245° ____ 3. Verify this identity: cos θ sec θ = 1. A. B. C. D. 0 = 0 ____ 4. Describe the translation in y = cos (x – ) – 3. A. right π units; down 3 units B. left π units; down 3 units C. right π units; up 3 units D. left π units; up 3 units ____ 5. Write this measure in radians: 80°. A. 80 B. C. D. ____ 6. Identify the amplitude and period of this function: y = −cos 2θ. A. 1, B. 2, C. D. ____ 7. Use either the Law of Sines or the Law of Cosines. In ΔRST, m∠R = 62°, m∠T = 29°, and TS = 12 in. Find RS. A. 6.6 in. B. 10.4 in. C. 12.2 in. D. 29.5 in. ____ 8. Simplify this expression: A. B. sin2 θ C. 0 D. 1 . ____ 9. Use the graph above to find the value of y = sin θ for the value radians. A. 0.5 B. 0 C. 1 D. −1 ____ 10. Write this measure in radians: 475°. A. B. C. D. 475 ____ 11. Use either the Law of Sines or the Law of Cosines. In ΔDEF, m∠F = 21°, d = 6 in., and f = 16 in. Find m∠D. A. 38.3° B. 19.6° C. 7.5° D. 26.7° ____ 12. Find the exact value of sin 22.5° . Use a half-angle identity. A. B. C. D. ____ 13. Write this measure in radians: −30°. A. B. C. D. ____ 14. Solve this equation for 0 ≤ θ < 2 : sin θ cos θ + sin θ = 0. A. 0, 1 B. , −1 C. 0, D. 0, ,2 ____ 15. Simplify this expression: sin θ sec θ cot θ. A. B. sin2 θ C. 0 D. 1 ____ 16. Find the value in radians of sin–1(–1.0). A. no solution B. −0.4794 C. −1.5708 D. −0.0500 ____ 17. Name two different times when the hands of a clock show an angle of radians. A. 1:00, 11:00 B. 2:00, 10:00 C. 3:00, 9:00 D. 4:00, 8:00 ____ 18. Identify the amplitude and period of this function: A. 2, 8 B. 4, 8 C. 4, 4 D. 2, 4 ____ 19. Evaluate this expression in radians: A. 45 B. C. D. 1 . . ____ 20. Write this measure in degrees: 8 radians. A. 180° B. 2880° C. 45° D. 1440° ____ 21. Use the graph above to find the value of y = sin θ for the value 330°. A. −1 B. 0 C. 1 D. −0.5 ____ 22. Find the exact value of tan 315°. Use the sum or difference identity. A. B. −1 C. 1 D. ____ 23. Write this measure in degrees: −3 A. −1080° B. −60° C. −180° D. −540° ____ 24. Find the exact sine value of 135°. A. B. C. D. radians. ____ 25. ΔRST is a right triangle with m∠S = 90°. ; Find cot R. A. B. C. D. ____ 26. Find the period of this function: A. 2 B. 4 C. 6 D. 8 ____ 27. Use either the Law of Sines or the Law of Cosines. In ΔDEF, m∠E = 65°, d = 19 in., and f = 25 in. Find e. A. 16.3 in. B. 14.2 in. C. 21.8 in. D. 24.2 in. ____ 28. Find the measure of an angle between 0° and 360° degrees coterminal with 575 degrees. A. 215° B. −145° C. 35° D. 145° ____ 29. Find the exact value of cos 75°. Use the sum or difference identity. A. B. C. D. ____ 30. A triangle with side lengths 6 in and 8 in and the measure of the angle between them is 51 degrees. What is the area of the triangle? A. 61.3 in.2 B. 81.9 in.2 C. 42.6 in.2 D. 18.7 in.2 ____ 31. ΔRST is a right triangle with m∠S = 90°. ; Find sin R. A. B. C. D. ____ 32. Find the exact cosine value of 135°. A. B. C. D. ____ 33. The period of a periodic function is 10 s. How many cycles does it go through in 45 s? A. cycle B. 4.5 cycles C. 450 cycles D. 2 cycles ____ 34. Solve this equation for A. B. C. D. . ____ 35. Find the measure of x to the nearest tenth. A. 27.4° B. 57.4° C. 95.2° D. 86.2° ____ 36. Find the maximum value of this function: A. 4 B. 3 C. −3 D. −4 ____ 37. Describe the phase shift and determine the value of “h” in the translation; . A. units to the left; h = − B. 1 unit to the left; h = −1 C. units to the right; h = D. units to the right; ____ 38. Find the exact value of cos 480°. Use a double-angle identity. A. 1 B. − C. 0 D. −1 ____ 39. Identify the graph of this function from 0 to 2 : y = 3 cos x. A. B. C. D. ____ 40. Identify the amplitude and period of this function: y = 3 sin 5θ. A. B. C. D. ____ 41. Find the minimum value of this function: A. 6 B. 8 C. 5 D. 0 ____ 42. In a circle, an arc of length 43.2 cm is intercepted by a central angle of radians. What is the radius of the circle? Round to the nearest whole number. A. 54 cm B. 17 cm C. 11 cm D. 35 cm ____ 43. Use either the Law of Sines or the Law of Cosines. In ΔDEF, d = 6 in., e = 7 in., and f = 12 in. Find m∠E. A. 111.7° B. 56.3° C. 89.8° D. 24.5° ____ 44. Write this measure in degrees: radians. A. 180° B. 150° C. 300° D. 15° ____ 45. Identify the domain and range of this function: y = 3 cos θ. A. d: −3 ≤ x ≤ 3; r: all real numbers B. d: all real numbers; r: −3 ≤ y ≤ 3 C. d: all real numbers; r: −1 ≤ y ≤ 1 D. d: −1 ≤ x ≤ 1; r: all real numbers ____ 46. ΔABC is a right triangle, with ∠C being the right angle. m∠A = 68°, b = 8, find a. A. 19.8 B. 2.4 C. 5.6 D. 12.2 ____ 47. Two buildings on level ground are 200 feet apart. From the top edge of the shorter building, the angle of elevation to the top of the taller building is 24°, and the angle of depression to the bottom of the taller building is 35°. How tall is each building? A. 100 ft, 200 ft B. 140 ft, 229 ft C. 150 ft, 215 ft D. 125 ft, 225 ft ____ 48. Find the measure of x to the nearest tenth. A. 36.5° B. 52.4° C. 91.1° D. 79.3° ____ 49. How many cycles does the sine function have in the interval 0 to 2 ? A. 0 B. 1 C. 2 D. 3 ____ 50. Identify the amplitude and period of this function: . A. , 3 B. none because no maximum or minimum value exist; C. n is an integer, D. none because no maximum or minimum value exist; Carefully review your answers on this progress test 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 the online test submission page in the presence of your proctor. The University of Nebraska is an equal opportunity educator and employer. ©2021, The Board of Regents of the University of Nebraska. All rights reserved. Second Year Algebra 2: Trigonometry Summary of Formulas Summary of Tables MTHH 040 TABLES Included in this section are two sets of tables. The first is the Table of Trigonometric Functions for angles written in degrees and the second is the Table of Trigonometric Functions for angles written in radians. Summary of Tables MTHH 040 Tables MTHH 040 Tables MTHH 040 Tables MTHH 040 Tables MTHH 040 Tables MTHH 040 Tables MTHH 040 Tables MTHH 040 blank page Tables MTHH 040 Course Name: Second Year Algebra 2 Course ID: MTHH040059 Student: Cole Dearmin Student ID: D48021432 Generated Date: May 31, 2021 Progress Test 3 Although the progress test is similar in style to the unit evaluations, the progress test is a closed-book test. It is important that you do your own work. Select the response that best completes the statement or answers the question. Your graphing calculator may be used on this progress test. You may also use scratch paper to work out the solutions. Use this link to access supplemental information that you may use as you take this Progress Test. ____ 1. How many cycles does the sine function, y = 3 sin θ, have in the interval from 0 to 2 ? A. 1 B. 2 C. 3 D. 4 From The above figure, from 0 to 2 pi we have one cycle. Answer option A. ____ 2. Find the measure of the angle in standard position. A. 115° B. −155° C. 245° D. −245° ____ 3. Verify this identity: cos θ sec θ = 1. A. B. C. D.0=0 ____ 4. Describe the translation in y = cos (x – ) – 3. A. right π units; down 3 units B. left π units; down 3 units C. right π units; up 3 units D. left π units; up 3 units ____ 5. Write this measure in radians: 80°. A. 80 B. C. D. ____ 6. Identify the amplitude and period of this function: y = −cos 2θ. A. 1, B. 2, C. D. ____ 7. Use either the Law of Sines or the Law of Cosines. m∠T = 29°, and TS = 12 in. Find RS. A. 6.6 in. B. 10.4 in. C. 12.2 in. D. 29.5 in. ____ 8. Simplify this expression: A. B. sin2 θ C. 0 D. 1 . In RST, m∠R = 62°, ____ 9. Use the graph above to find the value of y = sin θ for the value radians. A. 0.5 B. 0 C. 1 D. −1 ____ 10. Write this measure in radians: 475°. A. B. C. D. 475 ____ 11. Use either the Law of Sines or the Law of Cosines. In DEF, m∠F = 21°, d = 6 in., and f = 16 in. Find m∠D. A. 38.3° B. 19.6° C. 7.5° D. 26.7° ____ 12. Find the exact value of sin 22.5° . Use a half-angle identity. A. B. C. D. ____ 13. Write this measure in radians: −30°. A. B. C. D. ____ 14. Solve this equation for 0 ≤ θ < 2 : sin θ cos θ + sin θ = 0. A. 0, 1 , −1 B. C. 0, D. 0, ,2 ____ 15. Simplify this expression: sin θ sec θ cot θ. A. B. 2 sin θ C. 0 D. 1 ____ 16.Find the value in radians of sin–1(–1.0). A. no solution B. −0.4794 C. −1.5708 D. −0.0500 ____ 17. Name two different times when the hands of a clock show an angle of radians. A. 1:00, 11:00 B. 2:00, 10:00 C. 3:00, 9:00 D. 4:00, 8:00 18. ____ Identify the amplitude and period of this function: A. 2, 8 B. 4, 8 C. 4, 4 D. 2, 4 19. ____ Evaluate this expression in radians: A. 45 B. C. D. 1 . . ____ 20. Write this measure in degrees: 8 radians. A. 180° B. 2880° C. 45° D. 1440° ____ 21. Use the graph above to find the value of y = sin θ for the value 330°. A. −1 B. 0 C. 1 D. −0.5 ____ 22. Find the exact value of tan 315°. Use the sum or difference identity. A. B. −1 C. 1 D. ____ 23. Write this measure in degrees: −3 A. −1080° B. −60° C. −180° D. −540° ____ 24. Find the exact sine value of 135°. A. B. C. D. radians. ____ 25. RST is a right triangle with m∠S = 90°. ; Find cot R. A. B. C. D. ____ 26. Find the period of this function: A. 2 B. 4 C. 6 D. 8 ____ 27. Use either the Law of Sines or the Law of Cosines. In DEF, m∠E = 65°, d = 19 in., and f = 25 in. Find e. A. 16.3 in. B. 14.2 in. C. 21.8 in. D. 24.2 in. ____ 28. Find the measure of an angle between 0° and 360° degrees coterminal with 575 degrees. A. 215° B. −145° C. 35° D. 145° ____ 29. Find the exact value of cos 75°. Use the sum or difference identity. A. B. C. D. ____ 30. A triangle with side lengths 6 in and 8 in and the measure of the angle between them is 51 degrees. What is the area of the triangle? A. B. C. D. 61.3 in. 81.9 in. 42.6 in. 18.7 in. 2 2 2 2 ____ 31. RST is a right triangle with m∠S = 90°. ; Find sin R. A. B. C. D. ____ 32. Find the exact cosine value of 135°. A. B. C. D. ____ 33. The period of a periodic function is 10 s. How many cycles does it go through in 45 s? A. cycle B. 4.5 cycles C. 450 cycles D. 2 cycles ____ 34. Solve this equation for A. B. C. D. . ____ 35. Find the measure of x to the nearest tenth. A. 27.4° B. 57.4° C. 95.2° D. 86.2° ____ 36. Find the maximum value of this function: A. 4 B. 3 C. −3 D. −4 ____ 37. Describe the phase shift and determine the value of “h” in the translation; . A. units to the left; h = − B. 1 unit to the left; h = −1 C. units to the right; h = D. units to the right; ____ 38. Find the exact value of cos 480°. Use a double-angle identity. A. 1 B. − C. 0 D. −1 ____ 39. Identify the graph of this function from 0 to 2 : y = 3 cos x. A. B. C. D. ____ 40. Identify the amplitude and period of this function: y = 3 sin 5θ. A. B. C. D. ____ 41. Find the minimum value of this function: A. 6 B. 8 C. 5 D. 0 ____ 42. In a circle, an arc of length 43.2 cm is intercepted by a central angle of radians. What is the radius of the circle? Round to the nearest whole number. A. 54 cm B. 17 cm C. 11 cm D. 35 cm ____ 43. Use either the Law of Sines or the Law of Cosines. In DEF, d = 6 in., e = 7 in., and f = 12 in. Find m∠E. A. 111.7° B. 56.3° C. 89.8° D. 24.5° ____ 44. Write this measure in degrees: radians. A. 180° B. 150° C. 300° D. 15° ____ 45. Identify the domain and range of this function: y = 3 cos θ. A. d: −3 ≤ x ≤ 3; r: all real numbers B. d: all real numbers; r: −3 ≤ y ≤ 3 C. d: all real numbers; r: −1 ≤ y ≤ 1 D. d: −1 ≤ x ≤ 1; r: all real numbers ____ 46. ABC is a right triangle, with ∠C being the right angle. m∠A = 68°, b = 8, find a. A. 19.8 B. 2.4 C. 5.6 D. 12.2 ____ 47. Two buildings on level ground are 200 feet apart. From the top edge of the shorter building, the angle of elevation to the top of the taller building is 24°, and the angle of depression to the bottom of the taller building is 35°. How tall is each building? A. 100 ft, 200 ft B. 140 ft, 229 ft C. 150 ft, 215 ft D. 125 ft, 225 ft ____ 48. Find the measure of x to the nearest tenth. A. 36.5° B. 52.4° C. 91.1° D. 79.3° ____ 49. How many cycles does the sine function have in the interval 0 to 2 ? A. 0 B. 1 C. 2 D. 3 ____ 50. Identify A. B. C. D. the amplitude and period of this function: . ,3 none because no maximum or minimum value exist; n is an integer, none because no maximum or minimum value exist; Carefully review your answers on this progress test 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 the online test submission page in the presence of your proctor. The University of Nebraska is an equal opportunity educator and employer. ©2021, The Board of Regents of the University of Nebraska. All rights reserved. Second Year Algebra 2: Trigonometry Summary of Formulas Summary of Tables MTHH 040 TABLES Included in this section are two sets of tables. The first is the Table of Trigonometric Functions for angles written in degrees and the second is the Table of Trigonometric Functions for angles written in radians. Summary of Tables MTHH 040 Tables MTHH 040 Tables MTHH 040 Tables MTHH 040 Tables MTHH 040 Tables MTHH 040 Tables MTHH 040 Tables MTHH 040 Tables MTHH 040

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