Chapter 3 – Trig Formulas and Inverse Functions

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Topic 3.2

Tangent and Inverse Tangent

*Values of Tangent and Inverse Tangent* develops values of the tangent function for unit circle angles and the inverse tangent function. It is assumed that students are familiar with [latex]y= \sin^{-1} (x)[/latex] and [latex]y= \cos^{-1} (x)[/latex] which are found in *The Inverse Functions of Sine and Cosine*. It is also assumed that students are well-versed in handling the simplification of fractions within fractions involving radicals, for example, being able to simplify [latex]\frac{1/2}{\sqrt{3}/2}[/latex]. We are neutral on whether [latex]\frac{\sqrt 3}{3}[/latex] or [latex]\frac{1}{\sqrt 3}[/latex] is the preferred form for [latex]\tan (\frac{\pi}{6})[/latex] and present both. We intentionally chose not to address inverses for [latex]y = \cot (x)[/latex], [latex]y = \sec (x)[/latex], and [latex]y = \csc (x)[/latex] since these inverse functions are not widely used.

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