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The period of the tangent function is \(\pi\) because the graph repeats itself on intervals of \(k\pi\) where \(k\) is a constant. If we graph the tangent function on \(−\frac{\pi}{2}\) to \(\frac{\pi}{2}\), we can see the behavior of the graph on one complete cycle.
- Graphs of The Secant and Cosecant Functions
If we want to graph only a single period, we can choose the...
- Inverse Trigonometric Functions
Bear in mind that the sine, cosine, and tangent functions...
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- Graphs of The Secant and Cosecant Functions
The tangent and cotangent graphs satisfy the following properties: range: \((-\infty, \infty)\) period: \(\pi\) both are odd functions. From the graphs of the tangent and cotangent functions, we see that the period of tangent and cotangent are both \(\pi\).
The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent functions. Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less used.
The sine, cosine, secant, and cosecant functions have a period of [latex]2\pi[/latex]. Since the tangent and cotangent functions repeat on an interval of length [latex]\pi[/latex], their period is [latex]\pi [/latex] (Figure 9).
The sine, cosine, cosecant, and secant functions have a period of 2π. The tangent and cotangent functions have a period of π.
Period of a Tangent or Cotangent Function. As is the case with the sine and cosine function, if \(\omega\) is a nonzero constant that is not equal to \(1\) or \(-1\text{,}\) then the graph of \(y=\tan(\omega t)\) or \(y=\cot(\omega t)\) will be different than the periods of the graphs of \(y=\tan(t)\) and \(y=\cot(t)\text{.}\)
27 mar 2022 · Tangent and cotangent Graphs. The name of the tangent function comes from the tangent line of a circle. This is a line that is perpendicular to the radius at a point on the circle so that the line touches the circle at exactly one point. Figure \(\PageIndex{2}\)
