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
ﺻﻔﺤﺔ
4
ﯾﺤﻲ