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sin⁻¹(sin x) and its relatives

Inverse trigonometric functions

Concept 2 of 4 in Inverse Trigonometric Functions

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Think about this

A calculator gives sin⁡−1(sin⁡4π5)\sin^{-1}(\sin\frac{4\pi}{5}) =π5= \frac{\pi}{5}, not 4π5\frac{4\pi}{5}. Is the calculator wrong?