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Use a straightedge to draw an x- and y-axis. Use uniform lengths and mark (and label) your x-axis with multiples of 5 a. Graph 2 periods of the function y = sin x, starting with with x=0. b. On the same rectangular coordinate system, graph two periods of the reciprocal of the sine function, y = csc x, starting at x=0. To distinguish from the graph in part (a) either use a different color or use a dotted curve . . c. Show any vertical asymptotes using a dashed line -----. Be sure to use a straightedge. Full credit requires all instructions to be followed.

Use a straightedge to draw an x- and y-axis. Use uniform lengths and mark (and label) your x-axis with multiples of 5 a. Graph 2 periods of the function y = sin x, starting with with x=0. b. On the same rectangular coordinate system, graph two periods of the reciprocal of the sine function, y = csc x, starting at x=0. To distinguish from the graph in part (a) either use a different color or use a dotted curve . . c. Show any vertical asymptotes using a dashed line -----. Be sure to use a straightedge. Full credit requires all instructions to be followed.

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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### Instructions: 1. **Use a straightedge to draw an x- and y-axis.** - Use uniform lengths and mark (and label) your x-axis with multiples of \(\frac{\pi}{2}\). 2. **Graphing Tasks:** a. **Graph 2 periods of the function \( y = \sin x \), starting with \( x = 0 \).** b. **On the same rectangular coordinate system, graph two periods of the reciprocal of the sine function, \( y = \csc x \), starting at \( x = 0 \).** - To distinguish from the graph in part (a), either use a different color or use a dotted curve. c. **Show any vertical asymptotes using a dashed line.** - Ensure to use a straightedge for this step as well. 3. **Note:** - **Full credit requires all instructions to be followed.** ### Additional Explanation for Diagrams/Graphs: - **Sine Graph (\( y = \sin x \)):** - The sine function is periodic with a period of \(2\pi\). Therefore, for two periods, plot from \( x = 0 \) to \( x = 4\pi \). - Important points to label on the x-axis include \( 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi, \frac{5\pi}{2}, 3\pi, \frac{7\pi}{2}, \) and \( 4\pi \). - **Cosecant Graph (\( y = \csc x \)):** - The cosecant function is the reciprocal of the sine function. It has vertical asymptotes wherever the sine function is zero (i.e., at \( x = 0, \pi, 2\pi, 3\pi, \) and \( 4\pi \)). - The graph of \( y = \csc x \) will have vertical asymptotes at these points and will be undefined there. Between these asymptotes, the cosecant function will have parabolas opening upwards or downwards between the maximum and minimum points of the sine function. - **Vertical Asymptotes:** - Clearly mark and label the locations of the vertical asymptotes using a
Transcribed Image Text:### Instructions: 1. **Use a straightedge to draw an x- and y-axis.** - Use uniform lengths and mark (and label) your x-axis with multiples of \(\frac{\pi}{2}\). 2. **Graphing Tasks:** a. **Graph 2 periods of the function \( y = \sin x \), starting with \( x = 0 \).** b. **On the same rectangular coordinate system, graph two periods of the reciprocal of the sine function, \( y = \csc x \), starting at \( x = 0 \).** - To distinguish from the graph in part (a), either use a different color or use a dotted curve. c. **Show any vertical asymptotes using a dashed line.** - Ensure to use a straightedge for this step as well. 3. **Note:** - **Full credit requires all instructions to be followed.** ### Additional Explanation for Diagrams/Graphs: - **Sine Graph (\( y = \sin x \)):** - The sine function is periodic with a period of \(2\pi\). Therefore, for two periods, plot from \( x = 0 \) to \( x = 4\pi \). - Important points to label on the x-axis include \( 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi, \frac{5\pi}{2}, 3\pi, \frac{7\pi}{2}, \) and \( 4\pi \). - **Cosecant Graph (\( y = \csc x \)):** - The cosecant function is the reciprocal of the sine function. It has vertical asymptotes wherever the sine function is zero (i.e., at \( x = 0, \pi, 2\pi, 3\pi, \) and \( 4\pi \)). - The graph of \( y = \csc x \) will have vertical asymptotes at these points and will be undefined there. Between these asymptotes, the cosecant function will have parabolas opening upwards or downwards between the maximum and minimum points of the sine function. - **Vertical Asymptotes:** - Clearly mark and label the locations of the vertical asymptotes using a
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