Question
Question 13, 1.3.67 HW Scors: 59.15\%, 11.24 of 19 Points 0 of 1 Find the indicated function value. If it is undefined, say so. \[ \sec 0^{\circ} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \sec 0^{\circ}= \) \( \square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function is undefined.
Ask by Craig Ford. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \sec 0^{\circ} = 1 \)
Solution
To find \( \sec 0^{\circ} \), we'll use the definition of the secant function:
\[
\sec \theta = \frac{1}{\cos \theta}
\]
First, evaluate \( \cos 0^{\circ} \):
\[
\cos 0^{\circ} = 1
\]
Now, apply the definition of secant:
\[
\sec 0^{\circ} = \frac{1}{\cos 0^{\circ}} = \frac{1}{1} = 1
\]
**Answer:**
**A.** \( \sec 0^{\circ}= 1 \)
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Simplify this solution Beyond the Answer
The secant function, \(\sec \theta\), is the reciprocal of the cosine function. Since \(\cos 0^{\circ} = 1\), we find that: \[ \sec 0^{\circ} = \frac{1}{\cos 0^{\circ}} = \frac{1}{1} = 1 \] So the answer is A. \(\sec 0^{\circ} = 1\). It's like having a superhero in the world of trigonometry—when \( \theta \) is zero, \(\sec\) swoops in as a perfect one, saving the day! Just remember, the secant will be undefined if you try to find it at angles where cosine is zero, like \(90^\circ\) or \(270^\circ\). Keep an eye on those angles!
