Trigonometry/Functions

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Fundamental trigonometry functions[edit]

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

TrigTriangle.svg

Sine[edit]

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

Cosine[edit]

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

Tangent[edit]

  • 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]

  • Cotangent θ is the reciprocal of tangent θ:

Secant[edit]

  • Secant θ is the reciprocal of cosine θ:

Cosecant[edit]

  • Cosecant θ is the reciprocal of sine θ:


Other considerations[edit]

  • 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]

Quiz[edit]

Other resources[edit]

Basic Trigonometry (Youtube)
Basic Trigonometry II (Youtube)