5.4 Sum and Difference Formulas

How are sum and difference formulas helpful?

• They allow us to more easily evaluate and rewrite trigonometric functions/expressions
• They can be used to help verify identities
• They are useful when calculating expressions relative to waves (actual real world situations!)

For the sake of time and energy, all calculations of angles will be done in radians, but the same calculations work for degrees (variables for the angles will be x and y respectively).

Sine Formulas:

 

    

 

The switching of the original sign on the left hand side only changes the in between sign on the right hand side

 

 

Example:

 








 
 

 

Cosine Formulas:

 

 

The switching of the original sign on the left hand side only changes the in between sign on the right hand side

 

 

Example:

 

 

 

 

 

 

 

 

 

Tangent Formulas:

 

 

 
 

The switching of the original sign on the left hand sign changes the in between signs in both the numerator and the denominator of the right hand sign

 

 

Example:

 

 

 

 

 

 

 

 

 

 

Some Hints:

• If you are stuck on a problem, try drawing it out, especially if it's a triangle. Visualizing things will make it easier to imagine and solve.

• If you need to think of a way to rewrite a more difficult trigonometric problem, trial and error may be your only option.

 
 

• KNOW YOUR UNIT CIRCLE!!!