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For f(x) = -csc +1 , complete the following: Domain: Range : Vertical Asymptotes: Period:

For f(x) = -csc +1 , complete the following: Domain: Range : Vertical Asymptotes: Period:

Trigonometry (11th Edition)
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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For the function \( f(x) = -\csc\left(\frac{1}{2}\left(x - \frac{\pi}{3}\right)\right) + 1 \), complete the following: Domain: _________________________________________ Range: _________________________________________ Vertical Asymptotes: _________________________________________ Period: __________________ The background consists of a simple Cartesian coordinate system with horizontal and vertical axes, but it does not contain any specific graph or markings.
Transcribed Image Text:For the function \( f(x) = -\csc\left(\frac{1}{2}\left(x - \frac{\pi}{3}\right)\right) + 1 \), complete the following: Domain: _________________________________________ Range: _________________________________________ Vertical Asymptotes: _________________________________________ Period: __________________ The background consists of a simple Cartesian coordinate system with horizontal and vertical axes, but it does not contain any specific graph or markings.
**Topic: Graphing Trigonometric Functions** --- **Objective:** Use the Sine function to sketch one cycle of \( f(x) = -\csc \left( \frac{1}{2} \left( x - \frac{\pi}{3} \right) \right) + 1 \), and complete the following table. --- **Table Overview:** - **Sine Function Values:** - \( y = \sin x \) - \((0,0)\) - \(\left(\frac{\pi}{2}, 1\right)\) - \((\pi, 0)\) - \(\left(\frac{3\pi}{2}, -1\right)\) - \((2\pi, 0)\) --- ### Task: - **Given Function:** - \( f(x) = -\sin \left( \frac{1}{2} \left( x - \frac{\pi}{3} \right) \right) + 1 \) --- **Instructions:** 1. **Understand the Function Transformation:** - Amplitude, phase shift, frequency, and vertical shift aspects of the function. 2. **Plot Key Points:** - Identify and plot key points on the graph using the given table values of the sine function. 3. **Sketch the Graph:** - Draw one cycle of the transformed function using the plotted points as a guide. 4. **Complete the Table:** - Solve \( f(x) \) for the respective x-values mentioned for \( y = \sin x \). --- **Note:** Graphs are essential for visualizing how transformations affect trigonometric functions. Practice plotting to enhance your understanding of these concepts. ---
Transcribed Image Text:**Topic: Graphing Trigonometric Functions** --- **Objective:** Use the Sine function to sketch one cycle of \( f(x) = -\csc \left( \frac{1}{2} \left( x - \frac{\pi}{3} \right) \right) + 1 \), and complete the following table. --- **Table Overview:** - **Sine Function Values:** - \( y = \sin x \) - \((0,0)\) - \(\left(\frac{\pi}{2}, 1\right)\) - \((\pi, 0)\) - \(\left(\frac{3\pi}{2}, -1\right)\) - \((2\pi, 0)\) --- ### Task: - **Given Function:** - \( f(x) = -\sin \left( \frac{1}{2} \left( x - \frac{\pi}{3} \right) \right) + 1 \) --- **Instructions:** 1. **Understand the Function Transformation:** - Amplitude, phase shift, frequency, and vertical shift aspects of the function. 2. **Plot Key Points:** - Identify and plot key points on the graph using the given table values of the sine function. 3. **Sketch the Graph:** - Draw one cycle of the transformed function using the plotted points as a guide. 4. **Complete the Table:** - Solve \( f(x) \) for the respective x-values mentioned for \( y = \sin x \). --- **Note:** Graphs are essential for visualizing how transformations affect trigonometric functions. Practice plotting to enhance your understanding of these concepts. ---
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