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Homework Statement
State one known vertical asymptote of the graph of 1/secx
Homework Equations
None
The Attempt at a Solution
1/secx = cosx
Vertical asymptote of cos graph?
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SUMMARY
The vertical asymptote of the graph of 1/sec(x) is located at x = π/2. This is because 1/sec(x) is equivalent to cos(x), which does not have any vertical asymptotes. However, the function sec(x) does have a vertical asymptote at x = π/2, where the function is undefined due to division by zero. Therefore, the correct answer to the homework question is x = π/2.
PREREQUISITES- Understanding of trigonometric functions, specifically secant and cosine.
- Knowledge of vertical asymptotes in the context of rational functions.
- Familiarity with the unit circle and the behavior of trigonometric functions at specific angles.
- Basic algebraic manipulation of trigonometric identities.
- Study the properties of the secant function and its graph.
- Learn about the behavior of trigonometric functions near their asymptotes.
- Explore the concept of limits in relation to vertical asymptotes.
- Investigate other trigonometric functions and their asymptotic behavior.
Students studying trigonometry, mathematics educators, and anyone interested in understanding the behavior of trigonometric functions and their graphs.
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