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.
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