Finding principal and general solutions of trigonometric equations

Principal and general solution of
trigonometric equations
mathews.suman@gmail.com

The solutions lying between 0 and 2π for the trigonometric
equations are called principal solutions.
Ex
Find the principal solution of 2
3
sin x
2
3
3
sin 


AS
T C
sin is positive in the 2nd quadrant
2
3
)
3
sin( 


Principal solutions are
3
2
,
3

0
π/2
π
3π/2

Find the principal solution of cosec x = -1
sinx = -1
x = 3π/2
This is the only value in [ 0, 2π]
(principal solution)

General solution of sinx = 0 is x = nπ In
General solution of cos x = 0 is
2
)12( 

n
x
In
General solution of tanx = 0 is x = nπ In

Find the general solution of 0)
4
cos( 

x
2
)12(
4

 nx
42
)12(

 nx
In
422
2 

n
x
4

  nx

Find the general solution of 0)
12
sin( 

x


nx 
12
Innx  ,
12



General solution of sinx = sinα is
Innx n
 ,)1( 
General solution of cos x = cos α is
1,2  nnx 

General solution of tan x = tan α is
Innx  ,
Find the general solution of
2
1
2sin x
6
sin
2
1
2sin

x

6
)1(2

 n
nx 
12
)1(
2
 nn
x 
1n

Find the general solution of sin 9x = sin x
sin 9x – sinx = 0
)
2
sin(
2
)
cos(2sinsin
yxyx
yx


2 cos 5x sin 4x = 0

cos 5x = 0, sin 4x = 0
2
)12(5

 nx
10
)12(

 nx
nx 4
4
n
x  1n
,
*****************

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Finding principal and general solutions of trigonometric equations

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