The Angle Addition Identities (4.09)
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Transcript of The Angle Addition Identities (4.09)
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The Angle Addition Identities (4.09)
Thanks to:
Mr Richardson
Lexington High School
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1
α
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β
α
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sin α
β
α
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cos α
sin α
β
α
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cos α
sin β
sin α
β
α
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cos β
cos α
sin β
sin α
β
α
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sin (α+β)
cos β
cos α
sin β
sin α
β
α
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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1
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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1
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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1
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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1
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
sin( cos
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
sin( cos
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
sin( cos
sin( )cos( )
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
sin( cos sin( )=sin( )cos( )+
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
sin( cos sin( )=sin( )cos( )+
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
sin( cos sin( )=sin( )cos( )+
cos( )cos( )
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
sin( cos sin( )=sin( )cos( )+
cos( )cos( )
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
sin( cos sin( )=sin( )cos( )+
cos( )cos( ) sin( )sin( )
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cos (α+β)
(sin α+β)
cos β
cos α
sin β
sin α
β
α
sin( cos sin( )=sin( )cos( )+
-sin( )sin( )cos( + )=cos( )cos( )
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