IB Maths AA SL 3.6 Trigonometric Identities Questions

Practise using and deriving trigonometric identities, tracking restrictions, reducing equations to solvable forms and checking all valid branches.

Exam points

Apply sin²θ + cos²θ = 1 and related trigonometric ratios to simplify expressions or determine an unknown ratio without first finding the angle.
Use double-angle identities for sine and cosine to transform and solve trigonometric expressions, preserving the stated domain and signs.

[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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IB Maths AA SL 3.6 Trigonometric Identities Questions question 1