Name:_______________________Date:_______________
Trigonometry
Final Exam Review Sheet . All work must be shown. Just having answers is not sufficient to receive full credit on the review.
1. Solve the equation if possible: 3x – 2(x + 5) = 10
2. Solve the equation if possible: x² – 12 x + 30 = 0
3. Solve the equation if possible: 12t³ – 84t² + 120t = 0
4. Find the distance between the following two points: (-1, 4) and (2, 0)
5. Find the midpoint between the following two points (-2, 2) and (3, -10)
6. Determine the center and the radius of the following circle:
x² + y² – 20x – 10y + 100 = 0
7. Sketch the graph of y = 8 – x
8. Determine the domain of f(x) = Ö x + 2
9. Find the inverse of the function f(x) = x³ + 2
10. Convert 5p to degrees. Be sure to round your answer to two decimal places.
7
11. Convert 84°15’ to radians. Be sure to round your answer to 4 decimal places.
12. Find the reference angle of 640°
13. Evaluate the trigonometric function without the aid of a calculator: sin (5p)
3
14. Find the value of csc 270°
15. Given that the cos 29° = .8746, evaluate the cos 151°
16. Find the secant of 11p without the aid of a calculator
4
17. Change 320° to radians in terms of p
18. Change p to degrees
9
19. Write an algebraic expression for sec [arcsin (x – 1)]
20. Find the five remaining functions given that sin q = and cos q < 0
21. Find the period, amplitude, and five key points of y = 3 cos ( x + p ). Then sketch the graph.
22. Sketch y = sin x + 2
23. Sketch y = 2 tan x
24. Sketch y = 3csc (x – )
25. Sketch y = –2sec x
26. Sketch y = cot (x – )
27. Sketch y = log3 x
28. Evaluate arccos .28
29. Evaluate arctan (-1)
30. Find the exact value of cos(arctan 2) without the aid of a calculator.
31. Verify the identity. csc x – sin x = cos x cot x
32. Solve 3tan² x – 1 = 0 on the interval [0, 2p)
33. Solve cot x cos² x = 2 cot x on the interval [0, 2p)
34. Evaluate ln e³
35. Evaluate log27 9
36. A 20 foot ladder leaning against the side of a house makes a 75° with the ground. How far up the side of the house does the ladder reach?
37. From a 150-foot observation tower on the coast, a Coast Guard officer sights a boat in difficulty. The angel of depression of the boat is 4°. How far is the boat from the shoreline?
38. An amateur radio operator erects a 75-foot vertical tower for his antenna. Find the angle of elevation to the top of the tower at a point on level ground 50 feet from the base.
39. Find the remaining sides and angles of the triangle if
A = 24.3°, C = 54.6°, and c = 2.68
40. Find the remaining sides and angles of the triangle if a = 9, b = 12, c = 15
41. Use Heron’s formula to find the area of a triangle with sides of
a = 5, b = 7, c = 10
42. Find the trigonometric form of -4 + 4i
43. Find the standard form of 2(cos + i sin )
44. Use DeMoivre’s Theorem to find [5(cos 20° + i sin 20°)]³
Review Sheet Answers
1. 20 41. 4Ö2 cis 135°
2. 6 ±Ö 6 42. –1 + iÖ3
3. 0, 2, 5 43. 125 + 125iÖ3
4. 5 2 2
5. (.5 , -4)
6. center ( 10, 5) radius = 5
7. see graph
8. x ³ -2
9. f-1(x) = ³Ö x –2
10. 128.57˚
11. 1.4704
12. 80
13. -Ö3
2
14. -1
15. -.8746
16. -Ö 2
17. 16p
9
18. 20°
19. Ö - x² + 2x
-x² + 2x
20. cos q = - 60 / 61
tan q = -11/60
csc q = 61/11
sec q = - 61/60
cot q = - 60/11
21. amp. = 3
per. = 2p
key points: (-p, 3) ( -p/2 , 0) ( 0, -3 ) (p/2, 0) (p, 3)
22. See graph
23. See graph
24. See graph
25. See graph
26. See graph
27. See graph
28. 1.29 radians or 73.7°
29. –p/4
30. Ö 5 / 5
31. answers may vary
32. p/6 and 5p/6 and 7p/6 and 11p/6
33. p/2 and 3p/2
34. 2/3
35. 19.32 feet
36. 2145 feet
37. 56.3°
38. B = 101.1°, a »1.35 , b » 3.23
39. A»36.9°, B »53.1° , C »90°
40. 16.25 sq. units