Trigonometric Equations and General Values

 

Trigonometric equation

A trigonometric equation is an equation involving one or more trigonometric functions as a variable. The equation may be true for one or more values, but not every values of the variable.

The general solution of the equations sin x = k, cos x = k and tan x = k:

·        General solution of sin x = k(- 1 £ k £ 1).

Let q be the angle (preferably the smallest) whose sine is k, and then general solution is given by

              x = np ± (- 1)ⁿq, for all integral values of n.

              If k = 0, then x = np.

              If cosec x = k, x = np + (- 1) q

              If sin x = 1, then x =

              If sin x = - 1, then x =

·        General solution of cos x = k          (- 1 £  k £ 1)

              x = 2np ± q where q be the particular angle such that cos q = k.

              If k = 1, then x = 2np

              If sec x = k, then x = 2np ± q.

              If k = 0, then x =

              If k = - 1, then x = (2n + 1) p

·         General solution of tan x = k(- ¥ <  k < ¥)

              x = np + q, where q be the particular angle such that tan q = k.

              If k = 0, then x = np

              If cot x = k, then x = np + q.