IB Maths AI SL 3.3 Applications of trigonometry Question Bank

Practise IB Mathematics SL/HL 3.3 by applying applications of trigonometry methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 4]

Zheng models the height of a section of a rollercoaster.
She uses the function

f(x)=0.001 x^{3}-0.12 x^{2}+4.05 x+3, \text { for } 0 \leq x \leq 60

where x is the horizontal distance from the left-hand end of the section and f(x) is the vertical height. Distances are measured in metres.

Zheng's model is shown on the following graph of y=f(x).

Figure for Question SL 3.3—Applications of trigonometry question 1 — IB Maths AI SL

Point O has coordinates (0,0).

Find the angle of elevation from O to M .

Zheng wants to place advertising boards in front of this section of the rollercoaster. At four positions along the rollercoaster track, she records the horizontal distance from O and the vertical height of the track.

Her values are shown in the table and represented on the graph.

Table for Question SL 3.3—Applications of trigonometry question 1 — IB Maths AI SL

attempt to use inverse tangent
$\tan ^{-1}\left(\frac{y}{x}\right)$ $61.7^{\circ}\left(61.6907 \ldots{ }^{\circ}\right)$

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SL 3.3—Applications of trigonometry question 1