Study GuideTrigonometry–Inverse Functions and Equations1. Inverse Cosine and Inverse SineThe standard trigonometric functions—like sine and cosine—areperiodic. This means they repeatthe same values over and over. Because of this repetition, the same output value can come frommany different input angles.This creates a problem:inverse functions can only exist if a function is one-to-one. To solve this,mathematicians restrict the domains of sine and cosine so that each output corresponds to exactlyone input.1.1Why Trigonometric Functions Need RestrictionsFigure 1 Sine function is not one to one.For a function to have an inverse, it must beone-to-one, which means:1.Each value in the domain maps to exactly one value in the range2.Each value in the range comes from exactly one value in the domainThe sine function fails this test because the same y-value occurs at many different x-values. This iswhy the sine function, as normally defined,does not have an inverse.To fix this, we restrict the domain so the function becomes one-to-one.Preview Mode
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