IB DP Maths: AA HL复习笔记3.6.3 Double Angle Formulae

What are the double angle formulae?

• The double angle formulae for sine and cosine are:
  • These can be found in the formula booklet
• • The formulae for sin and cos can be found in the SL section
  • The formula for tan can be found in the HL section

How are the double angle formulae derived?

• The double angle formulae can be derived from the compound angle formulae
• Simply replace B for A in each of the formulae and simplify
• For example
  • Sin 2A = sin (A + A) = sinAcosA + sinAcosA = 2sinAcosA

How are the double angle formulae used?

• Double angle formulae will often be used with…
  • ... trigonometry exact values
  • ... graphs of trigonometric functions
  • ... relationships between trigonometric ratios
• • Solve
    • The equation will most likely be in the form of a quadratic
• To help solve trigonometric equations which contain tan 2θ
  • Substitute tan 2θ for the double angle identity
  • Rearrange, often this will lead to a quadratic equation in terms of tan θ
  • Solve
• Double angle formulae can be used in proving other trigonometric identities