Goniometric function

triangle
Triangle
The goniometric functions sinus (sin), cosinus (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cst) relate an angle of a right-angled triangle to ratios of two side lengths.

The following goniometric functions are defined:
  • sin(α) = BC / AB
  • cos(α) = AC / AB
  • tan(α) = BC / AC
  • cot(α) = AC / BC
  • sec(α) = AB / AC
  • csc(α) = AB / BC
where α is the angle between the line segments AB and AC.

The most common convention is to name inverse trigonometric functions using an arc- prefix:
  • α = arcsin(BC / AB)
  • α = arccos(AC / AB)
  • α = arctan(BC / AC)
  • α = arccot(AC / BC)
  • α = arcsec(AB / AC)
  • α = arccsc(AB / BC)
Some useful relationships are:

sin(α) = cos(90° - α)
sin(α) = -sin(180° - α)
sin(α)2 + cos(α)2 = 1

tan(α) = cot-1(α)
tan(α) = cot(90° - α)
tan(α) = -tan(180° - α)
tan2(α) + 1 = cos(α)-2
cot2(α) + 1 = sin(α)-2

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