Trigonometry/Functions

Fundamental trigonometry functionsEdit

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

 

SineEdit

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

CosineEdit

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

TangentEdit

  • 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:

CotangentEdit

  • Cotangent θ is the reciprocal of tangent θ:  

SecantEdit

  • Secant θ is the reciprocal of cosine θ:  

CosecantEdit

  • Cosecant θ is the reciprocal of sine θ:  


Other considerationsEdit

  • 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  

TableEdit

QuizEdit

Other resourcesEdit

Basic Trigonometry (Youtube)
Basic Trigonometry II (Youtube)