PC Senior Final Review Answers
-
Upload
tana-gilliam -
Category
Documents
-
view
25 -
download
3
description
Transcript of PC Senior Final Review Answers
![Page 1: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/1.jpg)
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
![Page 2: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/2.jpg)
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
![Page 3: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/3.jpg)
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
![Page 4: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/4.jpg)
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
![Page 5: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/5.jpg)
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
![Page 6: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/6.jpg)
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
![Page 7: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/7.jpg)
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
![Page 8: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/8.jpg)
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
![Page 9: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/9.jpg)
417. Suppose is acute and cos . Find sin .
5A A A
A4
53
sin3
5A
PC Senior Final Review Answers
![Page 10: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/10.jpg)
20. Evaluate 4sin cos .6 6
1 34
2 23
PC Senior Final Review Answers
![Page 11: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/11.jpg)
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
![Page 12: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/12.jpg)
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
![Page 13: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/13.jpg)
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
![Page 14: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/14.jpg)
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
![Page 15: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/15.jpg)
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
![Page 16: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/16.jpg)
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
![Page 17: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/17.jpg)
132. lim
x
x
x
lim lim1 1
x x
x
x
PC Senior Final Review Answers
![Page 18: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/18.jpg)
2
2
2
8 7 534. Find lim
4 9x
x x
x
PC Senior Final Review Answers
![Page 19: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/19.jpg)
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
![Page 20: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/20.jpg)
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
![Page 21: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/21.jpg)
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
![Page 22: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/22.jpg)
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
![Page 23: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/23.jpg)
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
![Page 24: PC Senior Final Review Answers](https://reader036.fdocuments.us/reader036/viewer/2022062517/56812cec550346895d91af95/html5/thumbnails/24.jpg)
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