Algebra and Trigonometry Review Material

Algebra and Trigonometry

Review Material

Department of MathematicsVanderbilt University

June 2, 2004

http://atlas.math.vanderbilt.edu/~pscrooke/calculus/calculus.html

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«_

�� ª õOEJKGPG PRG ItDLHG 1Q PRG G�JHGII1OQ Ì q � ¤ _hY Ì q � ¤ _h ] � Ì q � � ¤ _h] ì Ì q � ¤ aia í ¤ _h q aia I1QSG ìq�_ íÌ ] aia] ì q �_ í Ì ¤ ca q aia] ì q �_ í Ì ¤ m«a�� ª õOEJKGPG PRG ItDLHG OQ e LQV 1Q PRG GtDLP1OQ eÌ ¤ h_e ¤ Ì q ] ha Y

ha ] eÌ ¤ h_e ¤ Ì q ] �eÌ ¤ h_e � ¤ � Ì q �] �eÌ ¤ h_e ¤ mb� q mb ¤ ì Ì q ¤ ha í q ha] �e ¤ b�Ì ¤ ì q h_í Ì q ìmb ¤ ha í] �e ¤ b�Ì ¤ ì q h_í Ì q ha«a�O gG RLNG �e ¤ b�Ì ¤ ì q h_í Ì q ha«a ] ha `gR1SR I1EJK1 GI PO PRG GtDLP1OQ�e ¤ b�Ì ¤ ì q h_ íÌ ] ha ¤ ha«aOH �e ¤ b�Ì ¤ ì q h_ íÌ ] «b ¤ ha«a ] _rha n«m

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(-1, 0) (1, 0)

(0, 1)

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135

jRG LFONG LQUKGI LHG E GLIDHGV DI1QU ��"�� Y [Q LQUKG � ELM LKIO F G EGLIDHGVDI1QU �� Y jRG HLV1LQ E GLIDHGE GQP SOHHGIJ OQVI PO L V1IPLQSG LHODQV PRG S1HSDE ¡WGHGQSG T � T OW PRG DQ1P S1HSKG �� ] _� � YéGP DI E GLIDHG LQ LHS OQ PRG DQ1P S1HSKG IPLHP1QU LP �h` r� OW KGQUPR �ë LQV GQV1QU LPL JO1QP P Y �W gG VHLg L HLM WHOE PRG OH1U1Q PRHODUR JO1QP P T gG RLNG WOHE GV LQ LQUKG� T gRGHG � ] �ë HLV1LQI Yradians

P

(1,0)

θ4

π

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jRG WOKKOg 1QU PgO LQUKGI LHG PRG ILE G Y4

πradians45 OR

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� HLV1LQI ] hcr��hcr HLV1LQI ] h�mr À �hcr HLV1LQI ] mr À h��b HLV1LQI ] mr�� ª õOQNGHP ��ï HLV1LQI PO VGUHGGI Y

� HLV1LQI ] hcr�c« À � HLV1LQI ] c« À hcr�c�« HLV1LQI ] _cc�«�

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(x, y)

(1, 0)(-1, 0)

(0, 1)

(0, -1)

P

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45

2

11

2

1 «c

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2

1

2,( )

1

2x =

11

2y =π

4

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60

3

2

2

1

1«i

π

6

3

2x =

2

1y =

3

2

1

2

1( , )

12

x =

32

y =

12

32

1

( , )

π3

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π6

π4

π3

π3

2

π2

3

2,( 1

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1

2, 3

2 )(

(

2

1 , 0 )

0 , 1( )

-1 , 0( )

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π2π 0,

, )( 1 1

2

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III IV

x

y

II I

x>0

(0,0)

y>0

x<0y<0

x<0y>0x>0

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Tan

positivecot

positive

Cossecθ

positive

All

positive

θ θθ

θθ

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π3

π22π

3

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2π3

π20,

1

2

3

2

III

( , )

1

2

3

2,-( - )

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bm

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hypotenuse

θ

opposite

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h 1

2

θ

1 + 2 = h

h = 5

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Algebra and Trigonometry Review Material

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