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PC Senior Final Review Answers. PC Senior Final Review Answers. Law of Sines. PC Senior Final Review Answers. Law of Sines. NOT TO SCALE. PC Senior Final Review Answers. Law of Cosines. PC Senior Final Review Answers. PC Senior Final Review Answers. PC Senior Final Review Answers. - PowerPoint PPT Presentation
Citation preview
100 m
tan 2810
53 m0
.2
h
h
A B
C
28
PC Senior Final Review Answers
1. At a distance of 100 m, the angle of elevation to the top
of a fir tree is 28 . About how tall is the tree?
?h
sin 74 sin
4 5
5sin 74s
in4
P
P
P DNE
4
74
Q P
5
R
6. Find the indicated. Be alert to problems with no solutions
or two solutions.
5, 4, 74 , Find p q Q m P
PC Senior Final Review Answers
sin 23 sin
9 8
8sin 23sin
9
,13 90. 5 .72m Q
Q
Q
7. Find the indicated. Be alert to problems with no solutions
or two solutions.
9, 8, 23 , Find p q P m Q
8
23
Q P
9
R
NOT TO SCALE
PC Senior Final Review Answers
PC Senior Final Review Answers9. A has sides of length 5, 8, and 10. What is the measure
of its largest ?
5 8
10
x
2 2 2
1 2 1 22 cosOPP ADJ ADJ ADJ ADJ
100 25 64 2 5 8 cos
11 80cos
11cos
80
26297 ..9 , 1
x
x
x
x
, Law of CosinesSSS SAS
cos(
Sum and D
) cos cos sin sin
sin( ) sin cos cos s
ifference Formulas for Cosine a
in
nd Sine
10. Find the exact value of sin15 .
sin(45 30 ) sin 45 cos30 cos 45 sin 30
2 3
6 2
2 1
2 2 2 2
4
PC Senior Final Review Answers
PC Senior Final Review Answers
cos
Sum and Difference Formulas for Cosine and
( ) cos cos sin sin
sin( ) sin cos co
e
s sin
Sin
11. Simplify
cos 75 cos15 sin 75 sin15
cos 75 15 cos601
2
cos
Sum and Difference Formulas for Cosine and
( ) cos cos sin sin
sin( ) sin cos co
e
s sin
Sin
sin 75 cos15 cos 75 sin15
sin 75 15 sin 9 10
12. Simplify
PC Senior Final Review Answers
5 115. Find tan when tan .
4 3
151tan tan 4 / 334
5 1 2 / 31 tan tan 12
14 3
tan tantan
1 tan tan
Sum Formula for Tangent
PC Senior Final Review Answers
417. Suppose is acute and cos . Find sin .
5A A A
A4
53
sin3
5A
PC Senior Final Review Answers
20. Evaluate 4sin cos .6 6
1 34
2 23
PC Senior Final Review Answers
222. Evaluate 2cos 1.12
cos 212
cos6
3
2
2
2
2 2
cos 2 2cos 1
cos 2 1 2sin
cos 2 cos sin
PC Senior Final Review Answers
23. Find a formula for the nth term of the arithmetic sequence
3, 5, 7,...
Initial Term
2 1nt n
3
2
3
Difference
nt 2 1n
1 1nt t n d
PC Senior Final Review Answers
24. State whether the sequence is arithmetic, geometric,
or neither, and find a formula for .nt
10, 6, 2, 2,...
:
10 1 4
14 4n
n
Arithmetic
t n
t n
1 1nt t n d
PC Senior Final Review Answers
25. Find a formula for the term of the geometric sequence
3, 4.5, 6.75,.. .
nth
Initial Term 3
1.5Ratio
11
nnt t r
1 nn
tt r
r
PC Senior Final Review Answers
n
nt
2
3
5.1
3n
nt
2
32
2
6 21
27. In an arithmetic sequence, 6 and
16. Find .
t
t t
6 1
2 1
1 1
21
5 16
1 6
54 10
25 7
62 27 5
200
22
1 7
2
t t d
t t d
d d
t t
t
1 1nt t n d
PC Senior Final Review Answers
3 6 1128. In a geometric sequence, 12 and 96. Find .t t t
11
nnt t r 122
13 rtt
96516 rtt
1 2 5
3
31
12 96
12 96
8 2 3
tr r
r
r r t
110
11
10
3072
3 2
tt r
1Find & t r
PC Senior Final Review Answers
132. lim
x
x
x
lim lim1 1
x x
x
x
PC Senior Final Review Answers
2
2
2
8 7 534. Find lim
4 9x
x x
x
PC Senior Final Review Answers
2
21
2 235. Evaluate lim analytically,
1 or explain why the limit DNE.
x
x x
x
1
12 1
lim1 1x
x x
x x
PC Senior Final Review Answers
2
336. Sketch without using derivatives.
1
xy
x
3
1
( ) 0 at .
( ) 0 at .
f x
g xx
x
:Sign Analysis
x
y
(0) 3f
x
y
lim ?x
f x
g x
2
3 1lim lim 0
1x x
x
x x
PC Senior Final Review Answers
37. Find the equation of the line that is tangent to the curve
at the point 9,3 .y x
1/ 2 1/ 2
1 1
1 1( ) '( )
2 21
'(9)6
Point Slope Form of a Line:
13 9
6
f x x f x xx
f
y y m x x
y x
PC Senior Final Review Answers
3
2
38. , ( 2, 8). Find the equation of the tangent line.
'( 2) 3( 2)
8 12( 2
1
)
2
y x P
f
y x
PC Senior Final Review Answers
2 3
2 3
2
3
3
3
2
2
42. Find the derivative of the following equations:
(A) 4 sin
4
' 12 sin 4 cos
12 cos 4 sin'
cos
12 cos 4 sin
(B) cos
(C)
=cos
y x x x x
x x x xy
x
x x x x
x
y x x
xy
x
2' 2secn 2 2ta yy xx
PC Senior Final Review Answers
2
43. Use the definition of derivative to find the derivative of:
2y x x
2 2
0
2 2 2 2
0 0
0
0
2 2lim
2 2 2 2 2 2lim lim
lim 2 2 2 2
limx x
x x
x
x x x x x x
x
x x x x x x x x x x x x
x xx x x
f x x f x
x
PC Senior Final Review Answers