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Fundamental trigonometry functions[edit | edit source]

There are six trigonometric functions in Trigonometry: sine, cosine, tangent, cotangent, secant, and cosecant.

Sine[edit | edit source]

  • Sine θ is the length of the leg opposite θ over the length of the hypotenuse:

Cosine[edit | edit source]

  • Cosine θ is the length of the leg adjacent to θ over the hypotenuse:

Tangent[edit | edit source]

  • Tangent of θ is the length of the leg on the opposite side of the triangle from the angle θ over the length of the leg of the triangle adjacent to the angle θ:

These three can be memorized by use of the name of the princess "Soh Cah Toa," meaning:

  • "sine-opposite-hypotenuse
  • cosine-adjacent-hypotenuse
  • tangent-opposite-adjacent".

The remaining ratios are reciprocals of the previous ratios:

Cotangent[edit | edit source]

  • Cotangent θ is the reciprocal of tangent θ:

Secant[edit | edit source]

  • Secant θ is the reciprocal of cosine θ:

Cosecant[edit | edit source]

  • Cosecant θ is the reciprocal of sine θ:

Other considerations[edit | edit source]

  • Since the hypotenuse of a right triangle is always the longest side, and
  • If we divide both sides of each of these inequalities by the positive number , we get and
    or and

Table[edit | edit source]

Angle values[edit | edit source]

θ radians sinθ cosθ tanθ cotθ secθ cosecθ
0 0 1 0 undefined 1 undefined
30° π/6 1/2 2
45° π/4 1 1
60° π/3 1/2 2
90° π/2 1 0 undefined 0 undefined 1
180° π 0 -1 0 undefined -1 undefined
270° 3π/2 -1 0 undefined 0 undefined -1
360° 0 1 0 undefined 1 undefined

Quiz[edit | edit source]

Other resources[edit | edit source]

Basic Trigonometry (Youtube)
Basic Trigonometry II (Youtube)