Trigonometric Equations
Exercises:
1. Solve
=
30, 0 
Solution:
Given, 
+
3
Let 
a
|
|
30
+
30
30
+810
27
3
+810
27)
3(
27)0
27)(
Either 27=0 or 30
When 270
4a
3
a 
As, 0 <x<π, hence sine cannot be
negative
Or 
When, 
a =
As, 0 <x<π, hence sine cannot be
negative
Or 
.
2.
Solve 2
Solution:
We have:
2
|
2 |
Which gives
If we take
Again, if we
take
Therefore, the
possible solutions of above equations are
, 
where
.
3.
Solve 
Solution:
We have:
Dividing both sides by 2, we get
Or 
4.
Solve: 
Solution:
We have:
Dividing both sides by 2, we
get
5.
Solve: 
Solution:
We
have: 
Divide the equation
by 2
6.
Find the general solution of the following equation: 
Solution:
We have
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|
Or 
7.
Find general solution of the following equation:
Solution:
We have:
As, 
so
Z
Z
Solution:
We have
[
Solution:
|
[ |
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When 
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