تحميل كتاب الدائرة المثلثية

‫اﻟﺳﻧﺔ اﻟﺛﺎﻟﺛﺔ‬

‫ﻣﻠﺧص ﻓﻲ اﻟدوال اﻟﻣﺛﻠﺛﯾﺔ‬

‫اﻟﺪاﺋﺮة اﻟﻤﺜﻠﺜﯿﺔ‬ ‫) (‪ Sin‬و اﻟﺘﺮﺗﯿﺒﺔ ھﻲ ) ( ‪ cos‬اﻟﻔﺎﺻﻠﺔ ھﻲ‬

‫)) (‪A(cos( ),sin‬‬

‫ﺑﻌض اﻟﻌﻼﻗﺎت اﻟﺗﻲ ﺗﺧص اﻟداﻟﺔ )‪sin(x‬‬ ‫) ( ‪sin ( ) = 1 − cos‬‬ ‫)) ‪= (1 − cos(2‬‬ ‫‪Sin (0) = 0‬‬ ‫) داﻟﺔ ﻓردﯾﺔ ‪sin(− ) = −sin( ) … … … … … … (fonction impair‬‬ ‫) (‪Sin( ± ) = sin( )cos( ) ±sin( )cos‬‬ ‫) (‪Sin (2 )=2sin( )cos‬‬ ‫) (‬ ‫) (‬

‫زوارق‬

‫ﺻﻔﺤﺔ‬

‫‪1‬‬

‫=‬

‫ﯾﺤﻲ‬

‫اﻟﺳﻧﺔ اﻟﺛﺎﻟﺛﺔ‬

‫ﻣﻠﺧص ﻓﻲ اﻟدوال اﻟﻣﺛﻠﺛﯾﺔ‬

Sin (3 ) = 3Sin ( )-4sin ( ) Sin( ∓ ) = ±sin( ) Sin( )+sin( ) = 2sin(

)

(

)

Sin( )-sin( ) = 2cos(

)

(

)

Sin( )sin( ) = [cos( − ) −

( + )] Cos(x) ‫ﺑﻌض اﻟﻌﻼﻗﺎت اﻟﺗﻲ ﺗﺧص اﻟداﻟﺔ‬

( ) =1−

( )

= (1 +

(2 ))

cos (0) = 1 cos(− ) = cos( ) … … … … … … (fonction pair

‫)داﻟﺔ زوﺟﯾﺔ‬

cos( ± ) =cos( )cos( ) ∓sin( )cos( ) cos (2 )

= =2

( )− ( )−1

=1−2 = cos (3 )

( )

( ) ( ) ( )

= -3cos ( )+4cos ( )

cos( ∓ ) =− cos( ) cos( )+cos( ) =2cos( cos( )-cos( ) =−2si (

)

(

)

(

)

)

cos( )cos( )= [cos( − ) +

( + )] cos ‫ و‬sin‫ﺑﻌﺾ اﻟﻌﻼﻗﺎت اﻟﺘﻲ ﺗﺮﺑﻄﮭﻤﺎ‬

sin ( ) + cos ( ) = 1 ‫ﯾﺤﻲ‬

‫ﺻﻔﺤﺔ‬

2

‫زوارق‬

‫اﻟﺳﻧﺔ اﻟﺛﺎﻟﺛﺔ‬

‫ﻣﻠﺧص ﻓﻲ اﻟدوال اﻟﻣﺛﻠﺛﯾﺔ‬

sin( )cos( )= [sin(α + β) + sin(α − β)] cos( ) sin ( )= [sin(α + β) − sin(α − β)] cos( ± ) =∓ sin( ) Sin( ± )= cos( ) tan(x) ‫ﺑﻌض اﻟﻌﻼﻗﺎت اﻟﺗﻲ ﺗﺧص اﻟداﻟﺔ‬ ( )

( )=

( )

= −1 + =

( )

(

)

(

)

( )

=

( )

tan (0) = 0 tan(−θ) = −tan(θ) … … … … … … (fonction impair tan( ± ) = tan (2 )

( )± ∓

tan( ± ) =

(

( ) ( ) ( ∓ ) ( ∓ )

=

( ± )

±

( )

=∓ tan( )

( ) ( )

=

( ± ) ∓

tan( ) ±tan( ) =

‫ﯾﺤﻲ‬

( )

( )

=

tan( ∓ ) =

‫)داﻟﺔ ﻓردﯾﺔ‬

=∓

=∓ cot( )

( )

( )

( ± ) ( )

( )

‫ﺻﻔﺤﺔ‬

3

‫زوارق‬

‫اﻟﺳﻧﺔ اﻟﺛﺎﻟﺛﺔ‬

‫ﻣﻠﺧص ﻓﻲ اﻟدوال اﻟﻣﺛﻠﺛﯾﺔ‬

‫رﺳم اﻟدوال‬ ‫)‪sin(x‬‬

‫)‪Cos(x‬‬

‫)‪tan(x‬‬

‫زوارق‬

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‫ﯾﺤﻲ‬