Because there are only a few angles for which the values of the trigonometric functions are known exactly(

it is useful to have formulas that enable us to express other angles in ` terms of these angles.

Sum and Difference Formulas

These formulas allow an angle to be expressed as the sum or difference of two other angles.

Examples

Find

Explanation

Half Angle Formulas

Double Angle Formulas

Examples

Evaluate

Explanation

Product-to-Sum Formulas

Sum-to-Product Formulas

Try these exercises

Evaluate

1. 

   
   

2. 

   
   

3. 

   
   

4. 

   
   

5. 

   
   

6. 

   
   

Answers to questions:

1. 

   
   

2. 

   
   

3. 

   
   

4. 

   
   

5. 

   
   

6.