The Sine

sin(x) = x - x³/3! + x⁵/5! - x⁷/7! + ... (See Taylor Series)

     This is can also be stated as follows: (Explanation)

sin(x) = (e^xi - e^-xi)/2i

     x is the angle in radians, i is the imaginary number, and e is the base of the natural logarithm.


The Cosine

cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ... (See Taylor Series)

     This is can also be stated as follows:

cos(x) = (e^xi + e^-xi)/2

The Tangent

tan(x) = x + 2x^3/3! + 16x^5/5! + 272x^7/7! + 7936x^9/9! + ... (See Taylor Series)

     Since the tangent is opposite over adjacent, this is can also be stated as follows:

tan(x) = O/A = (O/H)/(A/H) = sin(x)/cos(x)
tan(x) = ((e^xi - e^-xi)/2i)/((e^xi + e^-xi)/2)
tan(x) = ((e^xi - e^-xi)/(e^xi + e^-xi))/(2i/2)
tan(x) = ((e^xi - e^-xi)/(e^xi + e^-xi))/i

tan(x) = -i*(e^xi - e^-xi)/(e^xi + e^-xi)

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