A geometry problem by Jessica Wang

Geometry Level 4

f ( x ) = 2 sin ⁡ x 2 + 3 cos ⁡ x 3 f(x)=2\sin\frac{x}{2}+3\cos\frac{x}{3} , x ∈ R x\in \mathbb{R} .

Find the smallest positive period of the above function, correct to 1 decimal place.


The answer is 37.7.

Jessica Wang by Jessica Wang , 22, United Kingdom

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1 solution

Jessica Wang
Jul 13, 2015

The period of 2 sin ⁡ x 2 2\sin\frac{x}{2} is 4 π 4\pi , and the period of 3 cos ⁡ x 3 3\cos\frac{x}{3} is 6 π 6\pi , therefore the required period is 12 π 12\pi , which is the least common multiple. And 12 π ≈ 37.7 12\pi\approx \boxed{37.7} .

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