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IB Maths AA SL 3.5 Unit circle & exact values

IB Maths AA SL 3.5 Unit circle & exact values
IB Mathematics: analysis and approaches guide, first assessment 2021

Practise finding exact sin, cos and tan values from identities, right-triangle reasoning and unit-circle symmetry.

How this is tested

  • use sin^2θ + cos^2θ = 1 with a given exact value to find the missing trigonometric ratio
  • apply quadrant or unit-circle symmetry, such as cos(180° - θ), to decide the sign of an exact value
  • use exact values in triangle work, choosing the correct side for the condition given

Question 4(b)

[Maximum number: 2]

The following diagram shows a non-right angled triangle ABC .

Figure for Question 4(b) — IB Maths AA SL

AB=5,BC=62, AC^B=θ\mathrm{AB}=5, \mathrm{BC}=6 \sqrt{2}, \mathrm{~A} \hat{\mathrm{C}} \mathrm{B}=\theta and BA^C=2θ\mathrm{B} \hat{\mathrm{A}} \mathrm{C}=2 \theta, where 0<θ<π20<\theta<\frac{\pi}{2}.

Hence, find sin⁡θ\sin \theta.

Point D is located on [AC][\mathrm{AC}] such that the area of triangle BCD is 2142 \sqrt{14}.