7) y = sec ¹ (x + 1) Ay --5--4 24 2 3x 3m 2 8) y = sin x/3 --6-5-4-3-2-1 3x 2 2 EN 2 K2 R -R 3x
7) y = sec ¹ (x + 1) Ay --5--4 24 2 3x 3m 2 8) y = sin x/3 --6-5-4-3-2-1 3x 2 2 EN 2 K2 R -R 3x
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°.
Related questions
Question
identify the domain and range of each then sketch the graph
![**Graphs of Inverse Trigonometric Functions**
The image features graphs of two inverse trigonometric functions. Below is a detailed description of each graph provided for educational purposes.
**Graph 1: \( y = \sec^{-1}(x + 1) \)**
- **Axes:** The horizontal axis is labeled as \( x \), and the vertical axis is labeled as \( y \).
- **Grid:** Both axes are marked with grid lines. The \( x \)-axis ranges from -6 to 6, and the \( y \)-axis ranges from \(-\frac{3\pi}{2}\) to \(\frac{3\pi}{2}\).
- **Scale:** The vertical axis is marked with increments of \(\frac{\pi}{2}\).
- **Graph Characteristics:** This graph represents the inverse secant function with a horizontal shift. The function is typically defined for \( x \geq 1 \) or \( x \leq -1 \), and it reflects periodic discontinuities typical of secant functions.
**Graph 2: \( y = \sin^{-1}\left(\frac{x}{3}\right) \)**
- **Axes:** The horizontal axis is labeled as \( x \), and the vertical axis is labeled as \( y \).
- **Grid:** Similar to the first graph, the \( x \)-axis ranges from -6 to 6, and the \( y \)-axis ranges from \(-\frac{3\pi}{2}\) to \(\frac{3\pi}{2}\).
- **Scale:** The vertical axis is also marked with increments of \(\frac{\pi}{2}\).
- **Graph Characteristics:** This graph represents the inverse sine function modified by a horizontal scaling factor. The typical domain for \( \sin^{-1}(x) \) is \([-1, 1]\), but due to the scaling, the domain here would be \([-3, 3]\).
These graphs demonstrate the behavior and transformation of inverse trigonometric functions, useful in understanding their applications in various fields, including physics and engineering.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ca94bf1-a3cb-4731-b664-e99ad6c24252%2F97fa15ca-1efb-45fc-90a6-0306d9fc304b%2Fr9opzhp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graphs of Inverse Trigonometric Functions**
The image features graphs of two inverse trigonometric functions. Below is a detailed description of each graph provided for educational purposes.
**Graph 1: \( y = \sec^{-1}(x + 1) \)**
- **Axes:** The horizontal axis is labeled as \( x \), and the vertical axis is labeled as \( y \).
- **Grid:** Both axes are marked with grid lines. The \( x \)-axis ranges from -6 to 6, and the \( y \)-axis ranges from \(-\frac{3\pi}{2}\) to \(\frac{3\pi}{2}\).
- **Scale:** The vertical axis is marked with increments of \(\frac{\pi}{2}\).
- **Graph Characteristics:** This graph represents the inverse secant function with a horizontal shift. The function is typically defined for \( x \geq 1 \) or \( x \leq -1 \), and it reflects periodic discontinuities typical of secant functions.
**Graph 2: \( y = \sin^{-1}\left(\frac{x}{3}\right) \)**
- **Axes:** The horizontal axis is labeled as \( x \), and the vertical axis is labeled as \( y \).
- **Grid:** Similar to the first graph, the \( x \)-axis ranges from -6 to 6, and the \( y \)-axis ranges from \(-\frac{3\pi}{2}\) to \(\frac{3\pi}{2}\).
- **Scale:** The vertical axis is also marked with increments of \(\frac{\pi}{2}\).
- **Graph Characteristics:** This graph represents the inverse sine function modified by a horizontal scaling factor. The typical domain for \( \sin^{-1}(x) \) is \([-1, 1]\), but due to the scaling, the domain here would be \([-3, 3]\).
These graphs demonstrate the behavior and transformation of inverse trigonometric functions, useful in understanding their applications in various fields, including physics and engineering.
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