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25 lines
752 B
Plaintext
25 lines
752 B
Plaintext
; Trigonometric functions as complex exponentials.
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; Use m4 Mathomatic instead for easy entry of these trig functions.
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; Based on Euler's identity: e^(i*x) = cos(x) + i*sin(x)
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; Variable x is an angle in radians.
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; Unity relationship: sin(x)^2 + cos(x)^2 = 1
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; sin(x) (sine of x) = cos(pi/2 - x)
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sin=(e^(i*x)-e^(-i*x))/(2i)
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; cos(x) (cosine of x) = sin(pi/2 - x)
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cos=(e^(i*x)+e^(-i*x))/2
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; tan(x) (tangent of x) = sin(x)/cos(x) = cot(pi/2 - x)
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tan=(e^(i*x)-e^(-i*x))/(i*(e^(i*x)+e^(-i*x)))
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; cot(x) (cotangent of x) = cos(x)/sin(x) = tan(pi/2 - x)
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cot=i*(e^(i*x)+e^(-i*x))/(e^(i*x)-e^(-i*x))
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; sec(x) (secant of x) = 1/cos(x) = csc(pi/2 - x)
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sec=2/(e^(i*x)+e^(-i*x))
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; csc(x) (cosecant of x) = 1/sin(x) = sec(pi/2 - x)
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csc=2i/(e^(i*x)-e^(-i*x))
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