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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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![The equation to be graphed is:
\[ y = 2 - 3 \sec \left( x - \frac{\pi}{5} \right) \]
### Graph Description:
- **Axes**: The graph features a standard Cartesian coordinate system with x and y axes. Both axes are labeled.
- **Scale**: The axes are marked with a uniform scale with labeled increments. The detailed scale is not specified numerically in the image.
- **Function Characteristics**:
- **Transformation**: The function is a transformation of the secant function.
- **Translation**: The graph is horizontally shifted by \(\frac{\pi}{5}\) units.
- **Vertical Stretch and Shift**: The secant function is vertically stretched by a factor of 3 and shifted downward by 2 units.
The graph of this function will typically show vertical asymptotes, corresponding to the points where the secant function is undefined due to the cosine function in the denominator being zero. These are important features to consider when graphing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f9e96de-8215-4532-a7d0-6f1fdf87f241%2F01685bba-40b0-49d5-9286-4e694f37db92%2F5kt4437_processed.png&w=3840&q=75)
Transcribed Image Text:The equation to be graphed is:
\[ y = 2 - 3 \sec \left( x - \frac{\pi}{5} \right) \]
### Graph Description:
- **Axes**: The graph features a standard Cartesian coordinate system with x and y axes. Both axes are labeled.
- **Scale**: The axes are marked with a uniform scale with labeled increments. The detailed scale is not specified numerically in the image.
- **Function Characteristics**:
- **Transformation**: The function is a transformation of the secant function.
- **Translation**: The graph is horizontally shifted by \(\frac{\pi}{5}\) units.
- **Vertical Stretch and Shift**: The secant function is vertically stretched by a factor of 3 and shifted downward by 2 units.
The graph of this function will typically show vertical asymptotes, corresponding to the points where the secant function is undefined due to the cosine function in the denominator being zero. These are important features to consider when graphing.
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