Useful Tables

Reference and conversions.


Unit Circle, SOHCAHTOA, and the Law of Sines

Sine, Cosine and Tangent (shortened to sin, cos and tan) are each a ratio of sides of a right angled triangle. For a given angle θ, each ratio stays the same no matter how big or small the triangle is.

Unit Circle

The six functions sine, cosine, tangent, cosecant, secant, and cotangent can be defined in several different ways.

The unit circle, SOHCAHTOA, and the 6 triangle functions.

The unit circle, SOHCAHTOA, and the 6 triangle functions.

Unit circle definitions for (r = 1)

  • sin θ = y
  • cos θ = x
  • tan θ = y / x
  • csc θ = 1 / y
  • sec θ = 1 / x
  • cot θ = x / y

The inverse trigonometry functions are sin-1, cos-1, tan-1, csc-1, sec-1 and cot-1. These are also written arcsin, arccos, arctan, arccsc, arcsec, and arccot. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios.

SOHCAHTOA

"SOHCAHTOA" is a way of remembering how to compute the sine, cosine, and tangent of an angle.

  • SOH stands for: sin = Opposite / Hypotenuse
  • CAH stands for: cos = Adjacent / Hypotenuse
  • TOA stands for: tan = Opposite / Adjacent

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Law of Sines

The law of sines is an equation relating the lengths of the sides of a triangle (of any shape) to the sines of its angles. According to the law:

a / sin(A) = b / sin(B) = c / sin(C)

where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the respective opposite angles. The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known -- a technique known as triangulation.

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