RECIPROCALS OF TRIGONOMENTRY

The reciprocals of these functions are named the cosecant (csc), secant (sec), and cotangent (cot), respectively:

${\displaystyle \csc A={\frac {1}{\sin A}}={\frac {\textrm {hypotenuse}}{\textrm {opposite}}}={\frac {c}{a}},}$

${\displaystyle \sec A={\frac {1}{\cos A}}={\frac {\textrm {hypotenuse}}{\textrm {adjacent}}}={\frac {c}{b}},}$

${\displaystyle \cot A={\frac {1}{\tan A}}={\frac {\textrm {adjacent}}{\textrm {opposite}}}={\frac {\cos A}{\sin A}}={\frac {b}{a}}.}$

The cosine, cotangent, and cosecant are so named because they are respectively the sine, tangent, and secant of the complementary angle abbreviated to "co-".^[30]

With these functions, one can answer virtually all questions about arbitrary triangles by using the law of sines and the law of cosines.^[31] These laws can be used to compute the remaining angles and sides of any triangle as soon as two sides and their included angle or two angles and a side or three sides are known