the angle addition identities (4.09)

34
The Angle Addition Identities (4.09) Thanks to: Mr Richardson Lexington High School

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The Angle Addition Identities (4.09). Thanks to: Mr Richardson Lexington High School. a. a. a. a. a. a. a. a. a. a. a. sin( a) cos (b). a. sin( a) cos (b). sin( b )cos( a ). a. sin( a) cos (b). sin( a+b )=sin( b )cos( a )+. sin( a) cos (b). a. sin( a+b )=sin( b )cos( a )+. - PowerPoint PPT Presentation

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Page 1: The Angle Addition Identities  (4.09)

The Angle Addition Identities (4.09)

Thanks to:

Mr Richardson

Lexington High School

Page 2: The Angle Addition Identities  (4.09)

1

1

α

Page 3: The Angle Addition Identities  (4.09)

1

11

β

α

Page 4: The Angle Addition Identities  (4.09)

1

11

sin α

β

α

Page 5: The Angle Addition Identities  (4.09)

1

11

cos α

sin α

β

α

Page 6: The Angle Addition Identities  (4.09)

1

11

cos α

sin β

sin α

β

α

Page 7: The Angle Addition Identities  (4.09)

1

11

cos β

cos α

sin β

sin α

β

α

Page 8: The Angle Addition Identities  (4.09)

1

11

sin (α+β)

cos β

cos α

sin β

sin α

β

α

Page 9: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 10: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 11: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 12: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 13: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 14: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 15: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 16: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 17: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 18: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 19: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 20: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 21: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 22: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 23: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

Page 24: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

sin( cos

Page 25: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

sin( cos

Page 26: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

sin( cos

sin( )cos( )

Page 27: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

sin( cos sin( )=sin( )cos( )+

Page 28: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

sin( cos sin( )=sin( )cos( )+

Page 29: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

sin( cos sin( )=sin( )cos( )+

cos( )cos( )

Page 30: The Angle Addition Identities  (4.09)

1

11

cos (α+β)

(sin α+β)

cos β

cos α

sin β

sin α

β

α

sin( cos sin( )=sin( )cos( )+

cos( )cos( )

Page 31: The Angle Addition Identities  (4.09)

1

11

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( )

Page 32: The Angle Addition Identities  (4.09)

1

11

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( )

Page 33: The Angle Addition Identities  (4.09)
Page 34: The Angle Addition Identities  (4.09)