There is a horizontal asymptote for tangent and cotangent.Group of answer choicesTrueFalse

Understanding Asymptotes for Trigonometric Functions

1. Definition of Horizontal Asymptotes: A horizontal asymptote refers to a line $y = c$ that the graph of a function approaches as $x$ approaches infinity or negative infinity.

2. Analysis of the Functions:

   • Tangent Function: The function $y = \tan(x)$ does not approach any particular value as $x$ approaches infinity or negative infinity. Instead, it oscillates between $-\infty$ and $+\infty$ at regular intervals (specifically at odd multiples of $\frac{\pi}{2}$).
   • Cotangent Function: Similarly, the function $y = \cot(x)$ also oscillates between $-\infty$ and $+\infty$, without approaching any specific value as $x$ approaches infinity or negative infinity.

3. Conclusion: Since neither the tangent nor the cotangent function approaches a finite limit as $x$ goes to infinity or negative infinity, they do not have horizontal asymptotes.

Final Answer

False - There is no horizontal asymptote for the tangent and cotangent functions.