0195136047.pdf

APPENDIX

D

Mathematical Relations

D.1Trigonometric Functions

D.2Exponential and Logarithmic Functions

D.3Derivatives and Integrals

D.4Series Expansions and Finite Series

D.1 TRIGONOMETRIC FUNCTIONS

sin(x±

π

2

)=±cos(x)

cos(x±

π

2

)=∓sin(x)

sin(x±y)=sin(x)cos(y)±cos(x)sin(y)

cos(x±y)=cos(x)cos(y)∓sin(x)sin(y)

sin( 2 x)=2 sin(x)cos(x)

cos( 2 x)=cos^2 (x)−sin^2 (x)

2 j sin(x)=ejx−e−jx

2 cos(x)=ejx+e−jx

2 sin(x)sin(y)=cos(x−y)−cos(x+y)

2 sin(x)cos(y)=sin(x−y)+sin(x+y)

2 cos(x)cos(y)=cos(x−y)+cos(x+y)

sin^2 (x)+cos^2 (x)= 1

2 sin^2 (x)= 1 −cos( 2 x)

2 cos^2 (x)= 1 +cos( 2 x)

4 sin^3 (x)=3 sin(x)−sin( 3 x)

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