IB Maths AA SL 3.6 Trigonometric identities Question Bank

Practise IB Mathematics SL/HL 3.6 by applying trigonometric identities 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: 3]

Let $f(x)=\cos 2 x$ and $g(x)=2 x^{2}-1$ .

Given that $(g \circ f)(x)$ can be written as $\cos (k x)$ , find the value of $k, k \in \mathbb{Z}$ .

$\quad(g \circ f)(x)=2(\cos (2 x))^{2}-1\left(=2 \cos ^{2}(2 x)-1\right)$
evidence of $2 \cos ^{2} \theta-1=\cos 2 \theta$ (seen anywhere)
$(g \circ f)(x)=\cos 4 x$
k=4

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SL 3.6—Trigonometric identities question 1