Trig Functions

Written by Jerry Ratzlaff on . Posted in Trigonometry

  • trig functionHypotenuse: The side opposite the right angle "C", is the hypotenuse "c".
  • Opposite Leg: The side opposite to the angle needed "A", is the opposite side "a".
  • Adjacent Leg: The side opposite the hypotenuse and next to the angle needed, is the adjacent side "b".

abbreviations

\(\large{ \ sine = sin }\)

\(\large{ \ cosine = cos }\)

\(\large{ \ tangent = tan }\)

\(\large{ \ cotangent = cot }\)

\(\large{ \ cosecant = csc }\)

\(\large{ \ secant = sec }\)

\(\large{ \ arcsine = arcsin }\)

\(\large{ \ arccosine = arccos }\)

\(\large{ \ arctangent = arctan }\)

\(\large{ \ arccotangent = arccot }\)

\(\large{ \ arccosecant = arccsc }\)

\(\large{ \ arcsecant = arcsec }\)

Trig Functions formula

\(\large{ \ sin \; \theta= \frac {opposite}{hypotenuse} }\)   

\(\large{ \ cos \; \theta= \frac {adjacent}{hypotenuse} }\)  

\(\large{ \ tan \; \theta= \frac {opposite}{adjacent} }\)  

\(\large{ \ csc \; \theta= \frac {hypotenuse}{opposite} }\) 

\(\large{ \ sec \; \theta= \frac {hypotenuse}{adjacent} }\)

\(\large{ \ cot \; \theta= \frac {adjacent}{opposite} }\)  

\(\large{ \ arcsin \; \theta= \frac {opposite}{hypotenuse} }\) 

\(\large{ \ arccos \; \theta= \frac {adjacent}{hypotenuse} }\)

\(\large{ \ arctan \; \theta= \frac {opposite}{adjacent} }\)

\(\large{ \ arccsc \; \theta= \frac {hypotenuse}{opposite} }\)

\(\large{ \ arcsec \; \theta= \frac {hypotenuse}{adjacent} }\)

\(\large{ \ arccot \; \theta= \frac {adjacent}{opposite} }\)