Page 95 - Numerical Analysis Using MATLAB and Excel

Chapter 3 Sinusoids and Phasors

)
tan ( 180°θ = – tan θ (3.43)
–
θ ( cos φ + ) = θcos φcos – sin θsin φ (3.44)

)
–
( cos θφ = θcos φcos + sin θsin φ (3.45)
φ
θ ( sin φ + ) = sin θcos + cos θsin φ (3.46)
θ
–
θ ( sin φ – ) = sin θcos φ cos sin φ (3.47)
θ
tan
tan
φ +
θ ( tan φ + ) = -------------------------------- (3.48)
1 – θtan φtan
θ
φ –
tan
tan
θ ( tan φ – ) = -------------------------------- (3.49)
1 + θtan φtan
cos 2 θ + sin 2 θ = 1 (3.50)
cos 2θ = cos 2 θ – sin 2 θ (3.51)
sin 2θ = 2sin θ θcos (3.52)

θ
2tan
tan 2θ = ---------------------- (3.53)
1 – tan 2 θ

2 1
cos θ = -- 1 +( - cos 2θ ) (3.54)
2

-- 1 –(
sin 2 θ = 1 - cos 2θ ) (3.55)
2
1 1
-
-
θcos φcos -- cos θ ( = φ + ) -- cos θ ( + φ – ) (3.56)
2 2
1 1
-
θcos φsin -- sin θ ( = φ + ) – --sin θ ( φ – ) (3.57)
-
2 2
1 1
sin θcos φ = -- sin θ ( φ + ) --- sin ( + θφ ) (3.58)
–
-
2 2
1 1
)
-
sin θsin φ = -- cos ( θφ – cos θ ( φ + ) (3.59)
–
--
-
2 2

3−8 Numerical Analysis Using MATLAB® and Excel®, Third Edition
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