Make a table using multiples of r/4 for x to sketch the graph of y = sin 2x from x = 0 to x = 2x.

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:**

Make a table using multiples of \(\pi/4\) for \(x\) to sketch the graph of \(y = \sin 2x\) from \(x = 0\) to \(x = 2\pi\).

**Table:**

| \(x\)      | \(y = \sin 2x\) |
|------------|-----------------|
| \(0\)      |                 |
| \(\pi/4\)  |                 |
| \(\pi/2\)  |                 |
| \(3\pi/4\) |                 |
| \(\pi\)    |                 |
| \(5\pi/4\) |                 |
| \(3\pi/2\) |                 |
| \(7\pi/4\) |                 |
| \(2\pi\)   |                 |

**Explanation:**

The table is designed to help plot the function \(y = \sin 2x\) using specific angles as inputs, defined in terms of \(\pi/4\). Each entry in the table corresponds to a multiple of \(\pi/4\), and students are expected to calculate or graphically determine the corresponding sine values after applying the doubling transformation to \(x\).

Filling in this table will involve calculating \(\sin(0)\), \(\sin(\pi/2)\), \(\sin(\pi)\), and so on, effectively illustrating the periodic and oscillatory nature of the sine wave at these intervals.
Transcribed Image Text:**Instructions:** Make a table using multiples of \(\pi/4\) for \(x\) to sketch the graph of \(y = \sin 2x\) from \(x = 0\) to \(x = 2\pi\). **Table:** | \(x\) | \(y = \sin 2x\) | |------------|-----------------| | \(0\) | | | \(\pi/4\) | | | \(\pi/2\) | | | \(3\pi/4\) | | | \(\pi\) | | | \(5\pi/4\) | | | \(3\pi/2\) | | | \(7\pi/4\) | | | \(2\pi\) | | **Explanation:** The table is designed to help plot the function \(y = \sin 2x\) using specific angles as inputs, defined in terms of \(\pi/4\). Each entry in the table corresponds to a multiple of \(\pi/4\), and students are expected to calculate or graphically determine the corresponding sine values after applying the doubling transformation to \(x\). Filling in this table will involve calculating \(\sin(0)\), \(\sin(\pi/2)\), \(\sin(\pi)\), and so on, effectively illustrating the periodic and oscillatory nature of the sine wave at these intervals.
After you have obtained the graph, state the number of complete cycles your graph goes through between 0 and 2π. 

[Input Box] cycle(s) 

**Graph/Diagram Description:**  
This section seems to be part of an educational instruction related to graph analysis, possibly involving trigonometric functions. You may need to plot a sine or cosine graph and determine how many complete waves or cycles occur from 0 to 2π radians.
Transcribed Image Text:After you have obtained the graph, state the number of complete cycles your graph goes through between 0 and 2π. [Input Box] cycle(s) **Graph/Diagram Description:** This section seems to be part of an educational instruction related to graph analysis, possibly involving trigonometric functions. You may need to plot a sine or cosine graph and determine how many complete waves or cycles occur from 0 to 2π radians.
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