Multiple angles

  • Multiple angles are formed by multiplying an angle by a positive integer.
  • The trigonometric functions of multiple angles can be expressed in terms of the trigonometric functions of the original angle.
    The multiple angle formulas are used to simplify trigonometric expressions and solve trigonometric equations.
  • The most commonly used multiple angle formulas are the double angle formulas, which can be used to find the values of trigonometric functions for angles that are twice the size of known angles.
  • The triple angle and half-angle formulas can also be used to find the values of trigonometric functions for angles that are three times or half the size of known angles.


Important Formulas to Remember in these Multiple angles

  • \( \sin2x=2\sin x\cos x \)
  • \( \cos2x=\cos^2x-\sin^2x=2\cos^2x-1=1-2\sin^2x \)
  • \( \tan2x=\frac{2\tan x}{1-\tan^2x} \)