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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