What is the value of sec e? (Picture is not to scale.) 3
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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what is the value of sec 0
![## Question 3
**What is the value of sec \( \theta \)? (Picture is not to scale.)**
Below is a diagram of a right triangle with vertices labeled by their lengths:
- One of the vertices angle is \( \theta \).
- The opposite side to \( \theta \) (opposite leg) is labeled as 3.
- The adjacent side to \( \theta \) (adjacent leg) is labeled as 4.
- The hypotenuse is labeled as 5.
\[
\begin{array}{c}
& 5 \\
& \diagup \theta \diagup \\
3 & \diagdown & 4 \\
\end{array}
\]
### Steps to Solve:
1. Recall the definition of secant in terms of a right triangle:
\[
\sec \theta = \frac{\text{hypotenuse}}{\text{adjacent side}}
\]
2. From the given triangle:
\[
\text{Hypotenuse} = 5
\]
\[
\text{Adjacent side to } \theta = 4
\]
3. Plug in these values into the secant formula:
\[
\sec \theta = \frac{5}{4}
\]
Hence, the value of \( \sec \theta \) is \( \frac{5}{4} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85c4a466-0fc8-4bec-adfa-0e2bd5c46b2f%2F087f7065-ef80-47c2-9684-3393d12b23b8%2F1xruvl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Question 3
**What is the value of sec \( \theta \)? (Picture is not to scale.)**
Below is a diagram of a right triangle with vertices labeled by their lengths:
- One of the vertices angle is \( \theta \).
- The opposite side to \( \theta \) (opposite leg) is labeled as 3.
- The adjacent side to \( \theta \) (adjacent leg) is labeled as 4.
- The hypotenuse is labeled as 5.
\[
\begin{array}{c}
& 5 \\
& \diagup \theta \diagup \\
3 & \diagdown & 4 \\
\end{array}
\]
### Steps to Solve:
1. Recall the definition of secant in terms of a right triangle:
\[
\sec \theta = \frac{\text{hypotenuse}}{\text{adjacent side}}
\]
2. From the given triangle:
\[
\text{Hypotenuse} = 5
\]
\[
\text{Adjacent side to } \theta = 4
\]
3. Plug in these values into the secant formula:
\[
\sec \theta = \frac{5}{4}
\]
Hence, the value of \( \sec \theta \) is \( \frac{5}{4} \).
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