Trig Identities

Unit Circle function values for angle theta. Use (x, y) with r=1

For right triangle trig, x = opposite side y = adjacent side r = hypotenuse

Reciprocal Identities:

                        

Quotient Identities:

                                                                 

Pythagorean Identities:

                                         

Negative angle identities:

                                                  

                                                 

Sum and Difference Identities

       

        

                          

Double -Angle Identities:

                         

or or

 

Power-Reducing formulas from Half-Angle Identities

Product to Sum

Sum to Product

        

In any triangle  , with sides  ,  , and  , Law of Sines ,

Law of Cosines  or  or

,

The substitution yields , and