Back to Explain symmetry and periodicity — Problem 1 · Task Set 69

HSF.TF.A.4 Tutor Intake — Symmetry and Periodicity of Trig Functions

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Grade 9·11 problems·~14 min·Common Core Math - HS Functions·group·hsf-tf-a-4

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A student claims that $\pi$ is the period of sine because $\sin(0) = 0$ and $\sin(\pi) = 0$ .
Which response correctly evaluates this claim?

The claim is correct — $\sin(0 + \pi) = \sin(0)$ confirms the period is $\pi$ .

The claim is incorrect. Period requires $f(x + T) = f(x)$ for ALL $x$ .
Counterexample: $\sin\!\left(\tfrac{\pi}{2} + \pi\right) = \sin\!\left(\tfrac{3\pi}{2}\right) = -1 \neq 1 = \sin\!\left(\tfrac{\pi}{2}\right)$ .

The claim is incorrect because $\pi$ is not where sine equals zero.

The claim is correct because the sine graph visually repeats after $\pi$ .