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Create a sketch of the function $y = \cos(\tan(x))$ for $-\pi \le x \leq \pi$, being sure to locate key turning points accurately.

You might wish to attempt this without resorting to IT.

Did you know ... ?

Whilst the properties of elementary functions might seem obvious, combinations of these can quickly lead to interesting behaviour which requires more thought to understand properly. Functions such as the one considered in the problem are part of the reason that calculus and functions are considered in more careful detail at university.

Whilst the properties of elementary functions might seem obvious, combinations of these can quickly lead to interesting behaviour which requires more thought to understand properly. Functions such as the one considered in the problem are part of the reason that calculus and functions are considered in more careful detail at university.