MTHH 0400 UN The Value and Angle of Radians Algebra Question

Course Name: Second Year Algebra 2Course ID: MTHH040059
Student: Daimon Gardner
Student ID: G83165467
Generated Date: October 27, 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. Describe the translation in y = cos (x + 1) – 2.
A. left 1 unit; down 2 units
B. left 1 unit; up 2 units
C. right 1 unit; down 2 units
D. right 1 unit; up 2 units
____ 2. 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
____ 3. 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
____ 4. Simplify this expression: sin θ csc θ.
A.
B. sin2 θ
C. 0
D. 1
____ 5. Find the measure of x to the nearest tenth.
A. 74.2°
B. 69.6°
C. 59.6°
D. 48.4°
____ 6. Find the exact value of cos 22.5° . Use a half-angle identity.
A.
B.
C.
D.
____ 7. Verify this identity: cos θ sec θ = 1.
A.
B.
C.
D. 0 = 0
____ 8. Identify the graph of this function from 0 to 2 : y = 3 cos x.
A.
B.
C.
D.
____ 9. Identify the amplitude and period of this function: y = 4 sin 3θ.
A.
B.
C.
D.
____ 10. Describe the phase shift and determine the value of “h” in the translation; y =
sin (x + 1).
A.
units to the left; h = −
B. 1 unit to the left; h = −1
C.
units to the right; h =
D. 1 unit to the right;
____ 11. 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
____ 12. A triangle with side lengths 11 in and 15 in and the measure of the angle
between them is 97 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
____ 13. Solve this equation for
A.
B.
C.
D.
____ 14. Find the value in radians of sin–1(–1.0).
A. no solution
B. −0.4794
C. −1.5708
D. −0.0500
____ 15. Find the exact cosine value of −30°.
A.
B.
C.
D.
.
____ 16. ΔRST is a right triangle with m∠S = 90°.
; Find sin R.
A.
B.
C.
D.
____ 17. Find the maximum value of this function:
A. 4
B. 3
C. −3
D. −4
____ 18. 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
____ 19. Simplify this expression:
A.
B. sin2 θ
C. 0
D. 1
____ 20. Find the period of this function:
A. 2
B. 4
C. 6
D. 8
.
____ 21. Write this measure in radians: –60°.
A.
B.
C.
D.
____ 22. Find the exact value of cos 75°. Use the sum or difference identity.
A.
B.
C.
D.
____ 23. Write this measure in degrees: −4
radians.
A. −720°
B. −1440°
C. −45°
D. −180°
____ 24. Write this measure in degrees: 8
radians.
A. 180°
B. 2880°
C. 45°
D. 1440°
____ 25. Find the measure of the angle in standard position.
A. −340°
B. −380°
C. −20°
D. 340°
____ 26. Use either the Law of Sines or the Law of Cosines. In ΔDEF, d = 10 in., e =
20 in., and f = 14 in. Find m∠E.
A. 111.8°
B. 56.3°
C. 89.8°
D. 24.5°
____ 27. ΔABC is a right triangle, with ∠C being the right angle. m∠A = 51°, b = 8,
find a.
A. 5.4
B. 5.7
C. 6.3
D. 9.9
____ 28. Identify the amplitude and period of this function:
.
A. n is an integer,
B. , 2
C. none because no maximum or minimum value exist;
D. none because no maximum or minimum value exist;
____ 29. Use either the Law of Sines or the Law of Cosines. In ΔDEF, m∠F = 43°, d =
16 in., and f = 24 in. Find m ∠D.
A. 38.3°
B. 19.6°
C. 7.5°
D. 26.7°
____ 30. Identify the domain and range of this function:
A. d: all real numbers; r:
B. d: −2 ≤ x ≤ 2; r: all real numbers
C. d:
; r: all real numbers
D. d: all real numbers; r: −2 ≤ y ≤ 2
.
____ 31. Use either the Law of Sines or the Law of Cosines. In ΔDEF, m∠E = 39°, d =
11 in., and f = 21 in. Find e.
A. 16.3 in.
B. 14.2 in.
C. 21.8 in.
D. 24.2 in.
____ 32. Evaluate this expression in radians:
.
A. 45
B.
C.
D. 1
____ 33. Solve this equation for 0 ≤ θ < 2 : sin θ cos θ – cos θ = 0. A. 0, B. C. D. ____ 34. How many cycles does the sine function, y = sin θ, have in the interval from 0 to 2 ? A. 1 B. 2 C. 3 D. 4 ____ 35. Find the exact value of cos 480°. Use a double-angle identity. A. 1 B. − C. 0 D. −1 ____ 36. Identify the amplitude and period of this function: y = −cos 2θ. A. 1, B. 2, C. D. ____ 37. Find the minimum value of this function: A. 6 B. 8 C. 5 D. 0 ____ 38. Find the exact value of tan 300°. Use the sum or difference identity. A. B. C. D. ____ 39. Find the measure of an angle between 0° and 360° degrees coterminal with 415 degrees. A. −125° B. −55° C. 125° D. 55° ____ 40. Write this measure in degrees: A. 288° B. 225° C. 144° D. 180° radians. ____ 41. How many cycles does the sine function have in the interval 0 to 2 ? A. B. 1 C. 2 D. 3 ____ 42. In a circle, an arc of length 51.8 ft is intercepted by a central angle of radians. What is the radius of the circle? Round to the nearest whole number. A. 9 ft B. 18 ft C. 28 ft D. 30 ft ____ 43. Find the measure of x to the nearest tenth. A. 43.0° B. 25.6° C. 39.8° D. 75.2° ____ 44. Write this measure in radians: 100°. A. 100 B. C. D. ____ 45. Identify the amplitude and period of this function: . A. 3, 3 B. 3, 10 C. 5, 10 D. 5, 3 ____ 46. Two buildings on level ground are 300 feet apart. From the top edge of the shorter building, the angle of elevation to the top of the taller building is 42°, and the angle of depression to the bottom of the taller building is 38°. How tall is each building? A. 234 ft, 504 ft B. 383 ft, 717 ft C. 184 ft, 385 ft D. 216 ft, 447 ft ____ 47. Find the exact sine value of 135°. A. B. C. D. ____ 48. ΔRST is a right triangle with m∠S = 90°. A. B. C. D. ____ 49. Write this measure in radians: 425°. A. B. 425 C. D. ; Find cot R. ____ 50. Use either the Law of Sines or the Law of Cosines. In ΔRST, m∠R = 35°, m∠T = 48°, and TS = 8 in. Find RS. A. 6.6 in. B. 10.4 in. C. 12.2 in. D. 29.5 in. 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