Question

The period of the function $f(x) = 2\cos\frac{1}{3}(x - \pi)$ is

• A. $6\pi$
• B. $4\pi$
• C. $2\pi$
• D. $\pi$

Answer 1

Answer: (A)

$6\pi$

Answer 2

$f(x) = 2\cos\frac{1}{3}(x - \pi)$ $= 2\cos\left( \frac{x}{3} - \frac{\pi}{3} \right)$

Now, since $\cos x$ has period $2\pi \Rightarrow$ $\cos\left( \frac{x}{3} - \frac{\pi}{3} \right)$ has period $\frac{2\pi}{\frac{1}{3}} = 6\pi$

$\Rightarrow$ $2\cos\left( \frac{x}{3} - \frac{\pi}{3} \right)$ has period $= 6\pi$.