3Daet.com | Double and Half Angle Formulas

Formulas and identities for double and half angles.

Mathematics.

Date Created:Friday January 26th, 2007 08:42 AM
Date Modified:Saturday August 02nd, 2008 12:24 PM

Double Angle formula

sin(2θ) = 2cosθsinθ

cos(2θ) = cos²θ - sin²θ

cos(2θ) = 1 - 2sin²θ

cos(2θ) = 2cos²θ - 1

              2tanθ
tan(2θ) =    ________
 
             1 - tan²θ

         1 - cos(2θ)
sin²θ =  ___________

             2

         1 + cos(2θ)
cos²θ =  ___________

             2

         1 - cos(2θ)
tan²θ =  ___________

         1 + cos(2θ)

Half Angle formula

            ____________
           /   1 - cosθ
sinθ/2 =  /   __________
         /
       ±√         2

            ____________
           /  1 + cosθ
cosθ/2 =  /   __________
         /
       ±√        2

            ____________
           /   1 - cosθ
tanθ/2 =  /   __________
         /
       ±√      1 + cosθ

Double Angle formula


Example:
sin195°


                 ___________
                /1 - cos390°
sin390/2  =    / _________
             ±√      2


                 ___________
                /1 - √3/2
sin390/2  =    / _________
             ±√      2