AAT HSEMESTER 2 REVIEW

Lets Get Rich

Rational s

Simplify

2

2

2 26 65 54

xx xxx

22( 1) 4

6 ( 1) 5( 1)

x x

x x x

2( 1)( 1) 4

6 ( 1) 5( 1)

x x x

x x x

4

15

Right Angle Trig

Solve the triangle

12 2cos cos ( ) 66.4

5 5A A

AB

C

2

5180 90 66.42 23.6 C

2 2 2

2

2 5

4 4

21 21

a

a a

Exponential Graphing

What is the horizontal asymptote for the function

3( ) 4 5xf x

y= -5

Bonus 100 Pts, what does the +3 do?

Shifts the graph 3 to the left.

Graphing Rationals

Find the vertical, horizontal asymptotes and holes of the function.

2

2

3 27( )

12

xf x

x x

23( 9) 3( 3)( 3) 3( 3)

( 4)( 3) ( 4)( 3) ( 4)

x x x x

x x x x x

VA: x=4

HA: y=3

Hole: x=-3

Rational Equalities

Solve the rational inequality

2 5 3

3 6 4y y

8 10 9

2

y

y

Probabilities

How many different ways can you pick a group of 3 from a set of 20 people?

1140

Right Angle Trig

Find cos(C)=

3cos

5C

AB

C

4

5

Right Angle Trig

Find csc(A)=

3sin( )

2A

AB

C

1

2

2csc()

3A

Unit Circle

The point is on unit circle in standard position. Find the six trig functions of the angle formed.

2 2sin csc 2

2 2

2 2cos sec 2

2 2tan 1 cot 1

B

2 2( , )2 2

Degrees/Radians

Convert to radians 120

2120

180 3

Degrees/Radians

Convert to degrees 7

9

7 180140

9

Logarithmic Equations

Solve 6 6log log 5 2x x

6log ( 5) 2x x

2 25 6x x

2 5 36 0x x

( 9)( 4) 0

9 4

9

x x

x or x

x

Degrees/Radians

Find a positive and a negative coterminal angle for 23 degrees

23 360 383

23 360 337

Logs!!!!

Write the following equations in log form.

3 7xe 3 log 7

3 ln 7ex

x

Law of Sines

Use the law of sines to solve the triangle .

180 37 48 95 C 48

B

37b

18m a

C

A

sin 95 sin 48

18 b

sin 95 18sin 48 13.4b b

sin 95 sin 37

18 a

sin 95 18sin 37 10.8a a

Logarithms

What is the domain and range for the basic exponential function.

Domain: All real numbers or, (-∞, ∞)Range: x>0 or, (0, ∞)

Right Angle Trig

The point (-1, 8) is on the terminal side of angle B in standard position. Find the six trig functions of B.

(-1,8)

-1

8

65

8 8 65 65sin csc

65 865

1 65cos sec 65

65658 1

tan 8 cot1 8

B B

B B

B B

Logarithmic Equations

Solve ln( 5) 12x

2( 5)x e

2 5x e

12.389x

Logarithmic Equations

Solve 3 3log (2 7) log (4 3)x x

2 7 4 3

4 2

x x

x

2

2

x

x

Probabilities

What is the probability of pulling a spade or a face card?

22/52=11/26