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

\(\ sine = sin \)

\(\ cosine = cos \)

\(\ tangent = tan \)

\(\ cotangent = cot \)

\(\ cosecant = csc \)

\(\ secant = sec \)

\(\ arcsine = arcsin \)

\(\ arccosine = arccos \)

\(\ arctangent = arctan \)

\(\ arccotangent = arccot \)

\(\ arccosecant = arccsc \)

\(\ arcsecant = arcsec \)

formula

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

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

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

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

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

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

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

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

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

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

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

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