IB Maths AA SL 3.7 Trigonometric Functions Questions

Practise reading and sketching periodic trigonometric graphs, recovering amplitude, period and phase parameters, and using models to interpret values or cycles.

Exam points

Read amplitude, midline, period and phase information from a sine, cosine or tangent graph or equation.
Sketch a periodic trig graph over a stated interval, labelling maxima, minima, intercepts, period and key coordinates.
Determine a, b, c and d in a sin(b(x+c))+d or equivalent from graph features, transformations or model data.
Use a periodic model such as tides, a wheel, a spring or population data to calculate a value, time, extremum or number of cycles and interpret it in context.

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Study SL 3.7—Trigonometric functions conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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Consider the function $f(x)=\frac{2}{\pi} \sin (3 \pi x)+2$ , where $0 \leq x \leq 2$ . The following diagram shows the graph of f.

Figure for Question IB Maths AA SL 3.7 Trigonometric Functions Questions question 1 — IB Maths AA SL

(a)

Write down the amplitude of f.

[ 3 ]

$0.636619 \ldots$

\text { (amplitude }=\text { ) } 0.637\left(=\frac{2}{\pi}\right)

(b)

Find the period of f.

[ 3 ]

$\frac{2 \pi}{3 \pi}$ OR 3 complete waves every 2 radians

(\text { period }=) 0.667\left(=\frac{2}{3}\right)

(c)

The point P has coordinates (1.63,2.16). State whether P lies above, below or on the graph of f. Justify your answer.

The line $L_{1}$ has equation x-6 y+11=0.

[ 3 ]

substituting to find f(1.63)

(f(1.63)=) 2.21564 \ldots

$2.21564 \ldots>2.16 \Rightarrow$ lies below (the graph of f )

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IB Maths AA SL 3.7 Trigonometric Functions Questions question 1

Question (a)

Question (b)

Question (c)