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TRIGONOMETRY FINAL EXAM REVIEW
CHAPTERS 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:
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Convert the degrees to radians and the radians to degrees.
The conversion factor for degrees to radians is:
The conversion factor for radians to degrees is:
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:
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21. Find the reference angle for (draw a sketch)
a. 215 degrees
b. 345 degrees
c. – 120 degrees
22. Find the distance between P(3, -2) and Q (5, 2).
The distance formula is:
23. The terminal side of an angle passes through the point (3, 4). Find the cosine of the angle.
Draw a sketch.
24. The terminal side of angle passes through the point (5, 3). Find the sine of the angle. Draw a
sketch
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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. Draw a sketch
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.
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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.) For the graph of y = 2 sin 3x + 4, find the following and then graph.
c. amplitude
d. vertical shift
e. phase shift
f. period
g. Graph from - 2π to 2π
32.) For the graph of y = 2 cos (x + π) find the following and then graph.
h. amplitude
i. vertical shift
j. phase shift
k. period
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l. Graph from - 2π to 2π
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.
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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:
B = 120
a = 15
b = 17
A = 43
a=8
b = 10
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
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42.) Prove:
43.) Prove :
44.)
1 + tan 2 Ө = sec 2 Ө
tan Ө
1 - cos 2 Ө
= sec Ө csc Ө
Prove: csc2 θ ( 1 - cos2 θ) = 1
45.) Prove: cot2 θ = csc2 θ – 1
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