Mathematical preliminaries - Continuous and Discrete Time Signals and Systems - page 793

Appendix A Mathematical preliminaries

A.1 Trigonometric identities

j t

e = cos t j sin t

= 1

2 [e j t

− j t ]

cos t + e

= 1

2j [e j t

− j t ]

sin t − e

t π
2

cos =∓ sin t

π
2

sin t = cos t

sin 2 t = 2 sin t cos t
cos 2 t + sin 2 t = 1
cos 2 t − sin 2 t = cos 2 t
cos 2 t = 1

2 (1 + cos 2 t )
sin 2 t = 1

2 (1 − cos 2 t )
cos 3 t = 1

4 (3 cos t + cos 3 t )
sin 3 t = 1

4 (3 sin t − sin 3 t )
cos( t θ ) = cos t cos θ ∓ sin t sin θ
sin( t θ ) = sin t cos θ cos t sin θ
tan ( t θ ) = tan t tan θ
1 ∓ tan t tan θ
sin t sin θ = 1

2 [cos( t − θ ) − cos( t + θ )]
cos t cos θ = 1

2 [cos( t + θ ) + cos( t − θ )]

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