Trigonometry

Double Angle Formulas

sin(2x) = 2sin(x)cos(x)

  • High school
  • about 3 min
  • 9 of 11 in the family
Not started
30°60°sin(2θ)=2sinθcosθ
θ = 30°
sin⁡(2⋅30°)=2sin⁡30°cos⁡30°=2⋅0.500⋅0.866=0.8660\sin(2\cdot30°) = 2\sin30°\cos30° = 2\cdot0.500\cdot0.866 = 0.8660
cos⁡(2⋅30°)=cos⁡230°−sin⁡230°=0.5000\cos(2\cdot30°) = \cos^230°-\sin^230° = 0.5000

Double angle formulas come from the addition formulas (sin(α+α)). The pink vector = double the angle of the blue vector on the unit circle.

Where it is taught