Additional Mathematics – Functions | e-Consult
Functions (1 questions)
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The sine function is periodic with period \(2\pi\); each value in the interval \([-1,1]\) is attained infinitely many times (e.g., \(\sin 0 = \sin \pi = \sin 2\pi = 0\)). Because multiple \(x\)-values give the same \(y\)-value, the function is not one‑to‑one and therefore lacks an inverse unless its domain is limited to an interval where it is monotonic, such as \([-\,\frac{\pi}{2},\frac{\pi}{2}]\).