Trig Final Exam Review: (Ch 1-4)
Name:__________________
Define the following:
1. Domain:
2. Range:
3. Function:
4. Vertical Line Test:
5. Standard Position
6. Quadrantal
7. Coterminal
8. Negative angle
9. Positive angle
Define the following in terms of x, y, and r:
10. Sine:
11. Cotangent:
12. Cosine:
13. Secant:
14. Tangent:
15. Cosecant:
Do the following conversions:
16. 132 degrees to radians
17. 245 degrees to radians
18. 2π/3 to degrees
19. 11π/6 to degrees
Answer the following:
20. What angle measurements (in degrees and radians) are in each quadrant?
I:
II:
III:
IV:
21. Find the reference angle for
a. 215 degrees
b. 345 degrees
c. – 120 degrees
22. Find the distance between P(3, -2) and Q (5, 2)
23. The terminal side of an angle passes through the point (3, 4). Find the cos of the
angle
24. The terminal side of angle passes through the point (5, 3). Find the sin of the
angle
25. The measure of an angle in standard position lies in Q III. The Tan of the angle is
½. Find the sin of the angle.
26. What are the ratios of the “special” triangles?
a. 30:60:90
b. 45:45:90
27. State whether the following functions are + or – in the quadrants:
Function
QI
QII
QIII QIV
Sin
Cos
Tan
Sec
Csc
Cot
28. The angle of depression from an airplane to the base of a monument is 60 degrees.
The altitude of the airplane is 100 meters. Determine the line of sight distance
from the plane to the base of the monument. Draw a sketch. Give your answer to
the nearest tenth of a meter.
29. In a right triangle A= 40, and c = 12. Find side b
30. In a right triangle a = 15 and b = 12. Find angle B
31. y = 2 sin 3x + 4
a. amplitude
b. vertical shift
c. phase shift
d. period
e. Graph this
32. y = 2 cos (x + π)
a. amplitude
b. vertical shift
c. phase shift
d. period
e. Graph this
33. A wheel rotates at 75 rpm. Find the angular velocity of the wheel.
34. A wheel spinning at an angular velocity of 200 rad/sec. Find the distance traveled
by a point 8 cm from the center during 2 sec.
35. Use sin (a + b) to find the exact value of sin 75 (no decimals)
36. Use cos (a – b) to find the exact value of cos 15 (no decimals)
37. In a triangle: A = 80 B = 75 and c = 40. Find the missing sides and angles.
38. In a triangle A = 65
b = 5 and c = 8. Find the missing sides and angles.
39. Find the number of solutions to the following triangles:
a. B = 120
a = 15
b = 17
b. A = 43
a=8
b = 10
c. A = 95
a = 12
b = 10
40. Find the area of the triangle if a = 2, b = 4, c =5
41. Find the area of a triangle if a = 15, b = 18 and C = 58 degrees
42. Prove: 1 + tan 2 Ө = sec 2 Ө
43. Prove:
tan Ө
1 - cos 2 Ө
= sec Ө csc Ө
44. Prove: csc2 θ ( 1 - cos2 θ) = 1
45. Prove: cot2 θ = csc2 θ – 1