Double-Angle and Half-Angle Formulas Rita Korsunsky
Double-Angle Formulas Let α = β : sin(α + β) = sin α cos β + cos α sin β sin(α + α) = sin α cos α + cos α sin α sin2α = 2 sin α cos α cos(α + β) = cos α cos β – sin α sin β cos(α + α) = cos α cos α – sin α sin α cos2α = cos2 α – sin2 α
Example 1 I
Example 2 Derive a formula for sin 4x in terms of functions of x.
Example 3
Half – Angle Formulas Use: Chose + or – depending on the quadrant in which lies
Example 4 I II
Example 5 II IV
Example 6 II III
Example 7 II III
Example 8 II IV
Example 9 Remember?