Trig Identities

Home
Up

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

 

 
 

The Unit Circle

 

 For right triangle trig, 

x = opposite side y = adjacent side 

r = hypotenuse

Trigonometric Identities and Formulas

Reciprocal Identities
  Cot theta = 1 over tan theta           sec theta = 1 over cos theta            csc theta = 1 over sin theta

Quotient Identities

tan theta = sin theta over cos theta                                 cot theta = cos theta over sin theta                                

Pythagorean Identities

sin squared + cos squared = 1                      tan squared + 1 = sec squared                    cot squared + 1 = csc squared

 

Negative angle identities

sin -theta = -sin theta                          cos -theta=cos theta                         tan -theta = -tan theta

csc -theta = -csc theta                        sec - theta = -sec theta                          cot -theta = -cot theta

Sum and Difference Identities

cos of difference of angles        cos of sum of angles

sin of difference of angles         sin of sum of angles

tan of difference of angles                           tan of sum of angles

Double -Angle Identities

                         

or or

 

Power-Reducing formulas from Half-Angle Identities

Product to Sum

Sum to Product

        

In any triangle  ABC, with sides  a,  b, and  c, Law of Sines Law of sines,

Law of Cosines law of cos (A) or law of cos (B) or law of cos (C)

 

,

The substitution yields , and

 

Click to access Mrs. Farber's email mailto:farberb@bucks.edu