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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ; Trigonometric functions as complex exponentials.
; Use m4 Mathomatic instead for easy entry of these trig functions.
; Based on Euler's identity: e^(i*x) = cos(x) + i*sin(x)
; Variable x is an angle in radians.
; Unity relationship: sin(x)^2 + cos(x)^2 = 1
; sin(x) (sine of x) = cos(pi/2 - x)
sin=(e^(i*x)-e^(-i*x))/(2i)
; cos(x) (cosine of x) = sin(pi/2 - x)
cos=(e^(i*x)+e^(-i*x))/2
; tan(x) (tangent of x) = sin(x)/cos(x) = cot(pi/2 - x)
tan=(e^(i*x)-e^(-i*x))/(i*(e^(i*x)+e^(-i*x)))
; cot(x) (cotangent of x) = cos(x)/sin(x) = tan(pi/2 - x)
cot=i*(e^(i*x)+e^(-i*x))/(e^(i*x)-e^(-i*x))
; sec(x) (secant of x) = 1/cos(x) = csc(pi/2 - x)
sec=2/(e^(i*x)+e^(-i*x))
; csc(x) (cosecant of x) = 1/sin(x) = sec(pi/2 - x)
csc=2i/(e^(i*x)-e^(-i*x))
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