IB Maths AI HL 3.7 Radian measure Question Bank

Practise IB Mathematics HL 3.7 by applying radian measure methods to exam-style questions.

[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 AHL 3.7 (HL)—Radian measure question 1 — IB Maths AI HL

On day t, where $t \in \mathbb{Z}$ , 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)=a \sin (b t)+c, t \in \mathbb{R} .

The graph of R is shown for one Martian year.

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

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

The angle, $\omega$ , 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 $\cos \omega=0.839 \tan \delta, 0 \leq \omega \leq \pi$ .

length of day $=24 \frac{2}{3}$ hours

Note: Award A1 for $\frac{2}{3}, 0.666 \ldots, 0 . \overline{6}$ or 0.667 .

\frac{2 \pi}{24 \frac{2}{3}}

Note: Accept $\left(\frac{360}{24 \frac{2}{3}}\right)$ .

=0.255 \text { radians }\left(=0.254723 \ldots, \frac{3 \pi}{37}, 14.5945 \ldots{ }^{\circ}\right)

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AHL 3.7 (HL)—Radian measure question 1