Download Fall Final exam review for Pre-Cal BC

Name: ________________________ Pre-Calculus Honors Fall Final Exam Review
*** ALL WORK AND ANSWERS MUST BE ON NOTEBOOK PAPER ***
7
to degrees.
2) Convert 115o to radian measure.
8
3) Determine two co-terminal measures
4) Determine two co-terminal measures
3
for
for -36o.
8
5) A sprinkler n a golf course fairway is set to spray water over a distance of 70 feet and rotates
through an angle of 120o. Find the area of the fairway watered by the sprinkler.
1) Convert
6) A terminal ray passes through (12, -5).
Find the value to all six trig. functions.
8) Evaluate each: cos
3
5
3
, sin
, tan
4
6
2
7) Find the value to all six trigonometric
5
functions if  =
.
3
11
 5 
9) Evaluate each: csc  
, sec
 , cot
6
 4 
1

10) If sin   and     , find
11) Evaluate cot 52.8o.
3
2
the remaining 5 trig functions.
12 – 15: Solve for x in each right triangle.
12)
13)
14)
x
12o
36
63o
x
x
7.5
2
15)
31
20
34
x
16) A steel cable zip-line is being constructed for a competition on a reality television show. One
end of the zip-line is attached to a platform on top of a 150 foot pole. The other end of the zip-line
is attached to the top of a 5 foot stake. The angle of elevation to the platform is 23o. How long is
the zip-line?
11
17) Find the reference angle if  = 309o.
18) Find the reference angle if  
.
3
19) Determine the quadrant when sec  < 0
20) Find all solutions in 0 <  < 2 for
3
sin   
and csc  < 0
.
2
21) Find all solutions in 0 <  < 2 for
22) Find all solutions in 0 <  < 2 for
tan   undefined
sec  2
23) Determine the amplitude of each:
1
f ( x)  sin x
4
g ( x)  5cos x
h( x)  7 tan x
24) Determine the period of each:
f ( x)  2sin 4( x   )
g ( x)   cos  3 x   1
2

h( x)  cot  x    3
3
2
25) Determine the phase shift of each:
f ( x)  2 cot 4( x   )


26) Graph y  2 cos  x    1
2

g ( x)   sec  3 x   1
2

h( x)  sin  x    3
3
2
1
27) Graph y  tan  2 x   3
2
29) Find the exact value of each:
1
arcsin  
2

2
cos 1  

 2 
tan 1 0
28) Graph y  sin 2( x   )
30) Find the exact value of each:
sec 1  2 
cot 1  1

arc csc  2


  
32) Find the exact value of arcsin  tan   
 2 

33) Graph y = 2 arcsin (2x)
34) Graph y  cos1 x  
35) A television camera at ground level is filming the lift-off of a space shuttle at a point 750
meters from the launch pad. Find the angle of elevation to the shuttle when it is 1200 meters high.
sin 
cos 

36) Simplify sin x  cot x cos x
37) Simplify
1  cos  sin 
2
2
38) Simplify cos x  sec x  1
39) Simplify cot  sec
31) Find the exact value of tan(arcos ½ )
40) Solve for all solutions 0 < x < 2
csc2 x  cot x  3  0
cos x
42) Verify graphically sec x  tan x 
1  sin x
44) Solve 2cos x + 1 = 0
46) Use the sum/difference formulas to
 
find the exact value of sin  
 12 
48) Find the exact value of
sin 420 cos120  sin120 cos 420
5 3
,
   2 then
13 2
find sin , cos 2, and tan 2
50) If cos  
52) Solve the triangle if:
C  102.30 , B  28.70 , b  27.4
41) Solve for all solutions 0 < x < 2
sec2 x  1  0
43) How many solutions are there for:
cos 2 x(2 cos x  1)  0
45) Solve sin3x = sin x
47) Use the sum/difference formulas to
find the exact value of tan 750
49) Find the exact value of

3

3
cos cos
 sin sin
16
16
16
16
51) Use the half-angle formula to find the
exact value of sin 105o.
53) Solve the triangle if:
A  420 , a  22, b  12
54) How many triangles are possible?
55) How many triangles are possible?
0
A  85 , a  15, b  25
A  20.50 , a  12, b  31
56) Because of Hurricane Ike, a tree grew so that it was leaning 4o from the vertical. At a point 35
meters from the tree, the angle of elevation to the top of the tree is 23o. Find the height of the tree.
0
57) Solve the triangle A  115 , c  10, b  15
58) Solve the triangle c  60, a  80, b  139
59) Find the area of the triangle if:
60) Find the area of the triangle if:
a  5, b  7, c  10
A  500 , c  2, b  4
60) Convert 2  2i 3 using cis notation
61) Convert 24 cis 300o.
62) Find the product of

 2  
 11  
 2cis  3   8cis  6  

 



63) Find the quotient of
4cis500
2cis 200
64) Identify the type of polar graph:
r 2  9sin 2
65) Identify the type of polar graph:
r  1  2cos
66) How many petals are on the rose:
67) How many petals are on the rose:
r = 4 cos 3
r = 3 cos 4

68) State 3 equivalent polar coordinates to (4, 105o).
69) Express in Complex Polar Form: 2 3 - 2 3i
70) Express your answer in rectangular form for:
æ
3p
3p ö æ
7p
7p ö
4 ç cos + isin ÷ ·5ç cos
+ isin ÷
12
12 ø è
12
12 ø
è
æ
11p
11p ö
10 ç cos
+ isin
18
18 ÷ø
è
71) Express your answers in rectangular form for
æ
p
pö
5 ç cos + isin ÷
9
9ø
è
8
æ
p
pö
72)Use DeMoivre’s Theorem to calculate ç cos + isin ÷ and express your answer in the polar
12
12 ø
è
form
73) Find the magnitude v and direction angle  for v = 5,-2
74) Determine if the vectors are parallel, orthogonal or neither: u = 6i +10 j v = 3i - 5 j
75) If u = -1,5 and v = -3,6 find 2u – 5v.
76) Initial point P (5, 2) and terminal point Q (-3, 7) are given, find the resultant vector.
77) If the angle measure between 2 forces is 1000 and one force is 50 pounds and the other is 72
pounds, find the resultant force.