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IB Maths AA SL 3.6 Trigonometric identities

IB Maths AA SL 3.6 Trigonometric identities
IB Mathematics: analysis and approaches guide, first assessment 2021

Practise rewriting trigonometric expressions with identities to prove results, form equations and simplify applied models.

How this is tested

  • use double-angle identities to rewrite expressions such as cos 2x in terms of sin x or cos x
  • transform tan θ into sin θ and cos θ, then use sin^2θ + cos^2θ = 1 to prove an identity
  • use identities to support later algebra, such as forming a quadratic in tan 22.5°

Question 3(a)

[Maximum number: 2]

Show that 3cos⁡2x+11sin⁡x=3+11sin⁡x−6sin⁡2x3 \cos 2 x+11 \sin x=3+11 \sin x-6 \sin ^{2} x.