First slide

Functions (XII)

Question

$π$ is the period of the function

Moderate

A

|sin x| + |cos x|
B

sin⁴x + cos⁴x
C

sin (sin x) + sin (cos x)
D

$\frac{1 + 2 \cos x}{\sin x (2 + \sec x)}$

Solution

The period of |sin x| + |cos x| and sin⁴x + cos⁴x is $\frac{π}{2}$ . sin (sin x) + sin (cos x) has period 2 $π$ . The function $\frac{1 + 2 \cos x}{\sin x (2 + \sec x)}$ can be written in a simplified form as $\frac{\cos x}{\sin x} = \cot x$ , so it has period $π$ .

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