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Advanced Math REVIEW for Spring Comprehensive Exam
1.) All work must be done on LOOSE LEAF with NO FRINGES!! (deduct 10 points).
2.) All work must be done IN ORDER (deduct 10 points).
3.) All work must be done IN PENCIL (deduct 10 points).
4.) You may NOT write on the back of loose leaf (deduct 10 points).
5.) Review must be turned in on the day of the final when you enter the auditorium (deduct all points if not
turned in at this time).
6.) Review is worth 100 points. In order to gain all points, all the above instructions must be followed. ALL
PROBLEMS MUST be completed to gain all possible points. Failure to follow any of the above will result
in the stated amount of deductions.
7.) Final exam will be TUESDAY, MAY 10 in the auditorium. You will be called out of class and be seated
according to a predetermined seating chart.
8.) You will be provided with a calculator and pencil, if you do not have your own. If you bring your own
calculator, you may have to turn it in to be checked.
S denotes the length of the arc of a circle of radius r subtended by the central angle . Find the
missing quantity.
1. r = 10 meters, = ½ radian, s = ?
2.
= 1/3 radian, s = 2 feet, r = ?
3. r = 5 miles, s = 3 miles,
4. r = 2 inches,
=?
= 30 , s = ?
Find the value of the six trigonometric functions of the angle in each figure. Give exact answers with
rational denominators.
5.
3
2
6.
2
4
7.
1
8.
1
Projectile Motion—The path of a projectile fired at an inclination to the horizontal with initial speed v0
is a parabola. The range R of the projectile, that is, the horizontal distance that the projectile travels, is
found by using the function
where g
32.2 feet per second per second
9.8 meters
per second per second is the acceleration due to gravity. The maximum height H of the projectile is given
by the function
.
Find the range R and maximum height H of the projectile. Round answers to two decimal places.
9. The projectile is fired at an angle of 45° to the horizontal with an initial speed of 100 feet per second.
10. The projectile is fired at an angle of 25° to the horizontal with an initial speed of 500 meters per second.
A point on the terminal side of an angle θ is given. Find the exact value of each of the six trigonometric
functions of θ.
11. (5, -12)
12. (2, -2)
13.
Use the even-odd properties to find the exact value of each expression. Do not use a calculator.
14. cos (-30 )
15. csc (-30 )
Write the equation of a sine function that has the given characteristics.
16. Amplitude: 3 Period: π
17. Amplitude: 3 Period: 2
Graph each function. Be sure to label key points and show one period.
18.
19.
20.
21.
22.
23.
Find the exact value of each expression.
   
24.sin 1 sin    
  10  
  5  
25.cos 1 cos    
  3 

3
26.sin 1  

 2 
1

27.sin  cos 1 
2


 1 
28.cot sin 1    
 2 



3 
29.cos sin 1  
 
 2  

30.Rewrite in terms of sine and cosine functions: tan  csc .
31.Multiply
cos 
1  sin 
by
.
1  sin 
1  sin 
32.Rewrite over a common denominator:
sin   cos  cos   sin 

.
cos 
sin 
Find the exact value of each expression.
33.
34.
35.
36.
37.
Use
the
information
given
about
.
the
angle
to
find
the
exact
value
of
38.
39.
Solve each equation on the interval 0< θ < 2π.
40.sin 2 (2 )  1  0
1

41.  cot   1  csc     0
2

2
42.2sin   3(1  cos  )
Solve the problem.
43. A security camera in a neighborhood bank is mounted on a wall 9 feet above the floor. What angle of depression
should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall?
44. A loading ramp 10 feet long that makes an angle of 18˚ with the horizontal is to be replaced by one that makes
and angle of 12˚ with the horizontal. How long is the new ramp?
Solve each triangle.
45. a = 2, c = 1, B = 10˚
46. b = 4, c = 1, A = 120˚
47. a = 4, b = 5, c = 3
Find the area of each triangle.
48. a = 2, c = 1, B = 10˚
49. b = 4, c = 1, A = 120˚
50. a = 3, b = 3, c = 2
Write in polar form. Express each argument in degrees
51. -1 + i
52. -2
53.
2  3i
Plot each point given in polar coordinates.
54. (4, 270˚)
55.  3,


3 

4 


2 

3 
56.  2, 
Use the vectors in the figure below to graph each of the following vectors.
w
u
v
57.
58.
59.
60.
u–v
v–w
2u – 3v + w
3v + u – 2w