Trigonometric Equations

Exercises:

1. Solve = 30, 0

Solution:

Given, +3

Let a

 

30

+30

30+810

273+810

27)3(27)0

27)(

Either 27=0 or 30

When 270

4a3

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

, then Or

Again, if we take

, then Or

Therefore, the possible solutions of above equations are

, where .

 

3. Solve

Solution:

We have:

Dividing both sides by 2, we get

Or

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

 

Or

 

7. Find general solution of the following equation:

Solution:

We have:

(

 

As, so

Z

Z

 

8. Solve:

Solution:

We have

[

[

 

9. Solve:

Solution:

We have

[

When