How to find the period of a tan function?
Understand the Problem
The question is asking how to determine the period of the tangent function in mathematics. The period of a function refers to the length of the interval over which the function repeats its values. For the tangent function, this involves understanding its properties and periodicity.
Answer
The period of the tangent function is $\pi$.
Answer for screen readers
The period of the tangent function is $\pi$.
Steps to Solve
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Identify the Tangent Function The tangent function can be expressed as $y = \tan(x)$.
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Understand the Definition of Periodicity The period of a function is the smallest positive value $P$ such that $f(x + P) = f(x)$ for all $x$ in the domain of the function.
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Determine the Period of Tangent For the tangent function, it is known that: $$ \tan(x + P) = \tan(x) $$ This equation holds true when $P = \pi$, since the tangent function has a periodicity of $\pi$.
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Conclusion Thus, the period of the tangent function is confirmed to be $\pi$.
The period of the tangent function is $\pi$.
More Information
The tangent function, unlike sine and cosine, has a shorter period of $\pi$. This means that it repeats its values every $\pi$ units along the x-axis. Understanding the periodicity helps in graphing the tangent function and solving related problems.
Tips
Common mistakes include confusing the period of the tangent function with that of sine or cosine, which is $2\pi$. Remember that the tangent function has a period of $\pi$.
