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IB Maths AA SL 3.8 Trigonometric Equations Questions

Practise solving trigonometric equations on finite intervals, retaining valid roots, checking branches and applying identities to periodic or physical models.

Syllabus
First assessment 2021
Course
Mathematics: analysis and approaches SL
Level
SL

Exam points

  • Solve a basic sine, cosine or tangent equation on a finite interval and list every solution in the required degree/radian form.
  • Reduce an equation to a quadratic or other algebraic equation in sin x, cos x or tan x, then back-substitute and retain only interval-valid roots.
  • Use reciprocal or trig identities and factorisation to simplify a more complex equation before solving it, checking excluded denominators and branches.
  • Use a periodic equation or model to find times, positions, threshold intervals or solution counts in the stated physical context.

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Study SL 3.8—Trigonometric equations conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AA SL 3.8 Trigonometric Equations Questions question 1

[Maximum number: 12]

The following diagram shows a square ABCD , and a sector OAB of a circle centre O , radius r. Part of the square is shaded and labelled R.

Figure for Question IB Maths AA SL 3.8 Trigonometric Equations Questions question 1 — IB Maths AA SL
AOB^=θ, where 0.5≤θ<π\mathrm{A} \hat{\mathrm{OB}}=\theta, \text { where } 0.5 \leq \theta<\pi

Question (a)

(a)

When θ=α\theta=\alpha, the area of the square ABCD is equal to the area of the sector OAB .

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Question (i)

(i)

Hence find α\alpha.

[ 4 ]

Question (b)

(b)

When θ=β\theta=\beta, the area of R is more than twice the area of the sector. Find all possible values of β\beta.

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