Trigonometry Solution – Problem 14: Find the minimum positive period of

Question

Period of Product Function

Find the minimum positive period of $f(x) = \sin\frac{x}{3}\cos\frac{x}{3}$ .

Using the double-angle formula:

$f(x) = \sin\frac{x}{3}\cos\frac{x}{3} = \frac{1}{2}\sin\frac{2x}{3}$

The period of $\sin\frac{2x}{3}$ is:

$T = \frac{2\pi}{\frac{2}{3}} = 3\pi$

$3\pi$

Translate the question into conditions (2 pts): domain/range/period/symmetry/monotonicity constraints are written correctly.
Key transformation or rewrite (2 pts): rewrite the function into a standard form (e.g. amplitude/phase/period) or reduce using identities.
Correct interval/parameter reasoning (2 pts): derive the correct inequalities or argument interval.
Final answer (1 pt): state the final set / interval / period clearly.

Listing properties ("periodic", "even") without applying them to the given function.