The document discusses principal and general solutions of trigonometric equations. It defines principal solutions as those between 0 and 2π and provides examples of finding principal solutions. It then defines the general solutions of trigonometric functions like sinx=0, cosx=0, and tanx=0. The document gives examples of finding general solutions of trigonometric equations and their relationship to principal solutions.
2. 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
mathews.suman@gmail.com
3. 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
mathews.suman@gmail.com
4. Find the principal solution of cosec x = -1
sinx = -1
x = 3π/2
This is the only value in [ 0, 2π]
(principal solution)
mathews.suman@gmail.com
5. 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
mathews.suman@gmail.com
6. Find the general solution of 0)
4
cos(
x
2
)12(
4
nx
42
)12(
nx
In
422
2
n
x
4
nx
mathews.suman@gmail.com
7. Find the general solution of 0)
12
sin(
x
nx
12
Innx ,
12
mathews.suman@gmail.com
8. General solution of sinx = sinα is
Innx n
,)1(
General solution of cos x = cos α is
1,2 nnx
mathews.suman@gmail.com
9. General solution of tan x = tan α is
Innx ,
Find the general solution of
2
1
2sin x
6
sin
2
1
2sin
x
mathews.suman@gmail.com
