IB Maths AA SL 3.7 Trigonometric functions Question Bank

Practise IB Mathematics SL/HL 3.7 by applying trigonometric functions 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: 9]

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 SL 3.7—Trigonometric functions 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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SL 3.7—Trigonometric functions question 1

Question (a)

Question (b)

Question (c)