This section discusses the graph of the secant function (shown below).
For ease of reference, some material is repeated
from the Trigonometric Functions.
$\displaystyle y = \sec x := \frac{1}{\cos x}$ (periodic with period $\,2\pi\,$) The cosine curve is shown in red. |
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Key ideas contributing to the graph:
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The graph of the secant function is easy to obtain as the reciprocal of the
cosine function.
The key ideas are illuminated below:
![]() the reciprocal of $\,1\,$ is $\,1\,$, so the points shown do not move |
![]() the reciprocal of $\,-1\,$ is $\,-1\,$, so the points shown do not move |
![]() zero has no reciprocal: where the cosine is zero, the secant has a vertical asymptote |
![]() the reciprocal of a small positive number is a large positive number |
![]() the reciprocal of a small negative number is a large negative number |
![]() the cosine curve is bounded between $\,\color{red}{1}\,$ and $\,\color{red}{-1}\,$; thus, the reciprocals all have size greater than or equal to $\,\color{green}{1}\,$ |
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. |
PROBLEM TYPES:
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