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On the axes below, make an appropriate scale and graph exactly one cycle of the trigonometric function y = -12 cosx. y Set the x and y axis labels. done x-axis label: в X π

On the axes below, make an appropriate scale and graph exactly one cycle of the trigonometric function y = -12 cosx. y Set the x and y axis labels. done x-axis label: в X π

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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--- ### Trigonometric Graphing Exercise #### Instructions: On the axes below, make an appropriate scale and graph exactly **one cycle** of the trigonometric function \( y = -12 \cos \left( \frac{1}{4} x \right) \). #### Steps: 1. **Set the x and y axis labels.** - Use the provided boxes to input the appropriate labels for the x-axis and y-axis. - Ensure the scale is balanced and appropriate for graphing one full cycle of the function. #### Graph Description: - The graph provided is a standard Cartesian plane with an x-axis (horizontal) and y-axis (vertical). - It is imperative to set your scale correctly to represent one cycle of the cosine function \( y = -12 \cos \left( \frac{1}{4} x \right) \). #### Important Details: - The amplitude of the function is 12. - The period of the function can be calculated by using the formula for the period of the cosine function, \( \text{Period} = \frac{2\pi}{\text{frequency}} \). In this case, the frequency is \( \frac{1}{4} \). - Hence, the period is \( \frac{2\pi}{\frac{1}{4}} = 8\pi \). Graphing one full cycle will involve plotting from \( x = 0 \) to \( x = 8\pi \). Remember to: 1. Mark the peak point at \( y = -12 \). 2. Identify the points where the function intersects the x-axis. 3. Illustrate the troughs and other periodic characteristics. #### Visual: - The graph includes a coordinate plane with grid lines to aid precision in plotting points. - Label boxes are provided near both axes to ensure axis labels can be accurately customized. --- Feel free to make use of this template as you work through the exercise and plot the function for better understanding.
Transcribed Image Text:--- ### Trigonometric Graphing Exercise #### Instructions: On the axes below, make an appropriate scale and graph exactly **one cycle** of the trigonometric function \( y = -12 \cos \left( \frac{1}{4} x \right) \). #### Steps: 1. **Set the x and y axis labels.** - Use the provided boxes to input the appropriate labels for the x-axis and y-axis. - Ensure the scale is balanced and appropriate for graphing one full cycle of the function. #### Graph Description: - The graph provided is a standard Cartesian plane with an x-axis (horizontal) and y-axis (vertical). - It is imperative to set your scale correctly to represent one cycle of the cosine function \( y = -12 \cos \left( \frac{1}{4} x \right) \). #### Important Details: - The amplitude of the function is 12. - The period of the function can be calculated by using the formula for the period of the cosine function, \( \text{Period} = \frac{2\pi}{\text{frequency}} \). In this case, the frequency is \( \frac{1}{4} \). - Hence, the period is \( \frac{2\pi}{\frac{1}{4}} = 8\pi \). Graphing one full cycle will involve plotting from \( x = 0 \) to \( x = 8\pi \). Remember to: 1. Mark the peak point at \( y = -12 \). 2. Identify the points where the function intersects the x-axis. 3. Illustrate the troughs and other periodic characteristics. #### Visual: - The graph includes a coordinate plane with grid lines to aid precision in plotting points. - Label boxes are provided near both axes to ensure axis labels can be accurately customized. --- Feel free to make use of this template as you work through the exercise and plot the function for better understanding.
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