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

Sketch and interpret y = sin x, y = cos x and y = tan x using amplitude, period, intercepts, asymptotes and domain restrictions.
Transform y = a sin(b(x + c)) + d in degrees or radians, determining parameters and applying the model to contexts such as tides or Ferris wheels.

[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 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)