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IB Maths AI HL Ahl 3 7 Hl Radian Measure Questions

Practise converting degrees to radians and using s = rθ and sector-area formulae to calculate unknown lengths, angles or areas with correct units.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

Exam points

  • Convert between degrees and radians and use radian measure consistently in arc-length and sector-area calculations.
  • Use s=rθ and sector-area formulae to find an unknown radius, angle, length or area.
  • Interpret the radian result in a diagram or applied context with correct units and exact or rounded values.

Learn this topic

Study AHL 3.7 (HL)—Radian measure conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AI HL Ahl 3 7 Hl Radian Measure Questions question 1

[Maximum number: 3]

A suitable site for the landing of a spacecraft on the planet Mars is identified at a point, A. The shortest time from sunrise to sunset at point A must be found.
Radians should be used throughout this question. All values given in the question should be treated as exact.
Mars completes a full orbit of the Sun in 669 Martian days, which is one Martian year.

Figure for Question IB Maths AI HL Ahl 3 7 Hl Radian Measure Questions question 1 — IB Maths AI HL

On day t, where t∈Zt \in \mathbb{Z}, the length of time, in hours, from the start of the Martian day until sunrise at point A can be modelled by a function, R(t), where

R(t)=asin⁡(bt)+c,t∈R.R(t)=a \sin (b t)+c, t \in \mathbb{R} .

The graph of R is shown for one Martian year.

Figure for Question IB Maths AI HL Ahl 3 7 Hl Radian Measure Questions question 1 — IB Maths AI HL

Find the angle through which Mars rotates on its axis each hour.

The time of sunrise on Mars depends on the angle, δ\delta, at which it tilts towards the Sun. During a Martian year, δ\delta varies from -0.440 to 0.440 radians.

The angle, ω\omega, through which Mars rotates on its axis from the start of a Martian day to the moment of sunrise, at point A , is given by cos⁡ω=0.839tan⁡δ,0≤ω≤π\cos \omega=0.839 \tan \delta, 0 \leq \omega \leq \pi.

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