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Harmonic Form
Rcos(θ + a) or Rsin(θ + a)
Uses trig angle formulae
Example: 2sin x + 5cos x = Rsin(x + a)
2sin x + 5 cosx = Rsin(x)cos(a) + Rsin(a)cos(x)
Rcos(a) = 2, Rsin(a) = 5; tan(a) = 5/2 --> tan-1(5/2) = 68.2°
R2cos2(x) + R2sin2(x) = 22 + 52 R2(cos2(x) + sin2(x)) = R2(1) = 22 + 52 = 29 R = √29
= √29cos(x + 68.2°)
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Trigonometry: Angles
Compound angles:
sin(A + B) = sinAcosB + cosAsinB
cos(A + B) = cosAcosB - sinAsinb [take note of signs]
tan(A + B) = (tanA + tanB) / (1 - tanAtanB) [take note of signs]
Double angles:
sin2x = 2sinxcosx
tan2x = (2tanx) / (1 - tan²x)
cos2x = cos²x - sin²x [...or...] 2cos²x - 1 [...or...] 1 - 2sin²x
Triple angles:
sin3x = sinx - 4sin³x
cos3x = 4cos³x - 3cosx
tan3x = (3tan - tan³x) / (1 - 3tan²x)
