pc senior final review presentation

100 m

tan 2810

53 m0

.2

h

h

A B

C

28

PC Senior Final Review Presentation

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

SohCahToa

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


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 Presentation9. 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



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


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


417. Suppose is acute and cos . Find sin .

5A A A

A4

53

sin3

5A


20. Evaluate 4sin cos .6 6

1 34

2 23


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


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


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


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


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


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


132. lim

x

x

x

lim lim1 1

x x

x

x


2

2

2

8 7 534. Find lim

4 9x

x x

x


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


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


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


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


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


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


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