Definition: Tangent of a Real Variable

Let \(x\in\mathbb R\) be any real number. The tangent of \(x\) is a function \(\tan:\mathbb R\mapsto\mathbb R\) defined as the ratio of the sine and cosine of $x$, formally,


The tangent function has is demonstrated in the following figure:

  1. Proposition: Additivity Theorem of Tangent
  2. Proposition: Derivative of Tangent

Propositions: 1 2 3

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  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983