**Problem 2: Graphing a Sine Function**Graph the function \( y = 1 + 2\sin\left(\frac{1}{2}x - \pi\right) \) over the interval \( 0 \leq x \leq 6\pi \).**Function Analysis:**1. **Transformation Basics:** - The function is a transformed sine wave. - The amplitude of the standard sine function is modified by a factor of 2, which means the graph will vertically stretch by 2. - There is a vertical shift up by 1 unit, which affects the midline of the graph. - The phase shift is determined by the \(- \pi\) inside the sine function, translating the graph to the right by \(\pi\) units. - The horizontal dilation is caused by the \(\frac{1}{2}\) within the function, which increases the period of the sine wave.2. **Period and Phase:** - The standard period of \( \sin(x) \) is \( 2\pi \). - For \( \frac{1}{2}x \), the period is \(\frac{2\pi}{\frac{1}{2}} = 4\pi\). - Thus, every cycle of the sine wave completes over \( 4\pi \).3. **Graph Details:** - Start plotting at \( x = \pi \) due to the phase shift. - The maximum point of the graph will be at \( y = 3 \) (1 + amplitude of 2), and the minimum point will be at \( y = -1 \) (1 - amplitude of 2). - The midline of the wave is at \( y = 1 \).These details will help in understanding the graphical representation of the given function over the specified interval.

Answered: Image /qna-images/answer/0b8dc7a5-1056-4f13-8249-c4d34149efd7.jpg

Answered: 2. Graph y = 1+ 2sin (x- n) on 0 < x <…

2. Graph y = 1+ 2sin (x- n) on 0 < x < 6TI.

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°.

Similar questions

Trigonometry Question
4. LaDainian graphed the cubic function g(x) = x³ – 4x², and then vertically translated the graph 1 unit up. Does the resulting graph ha fewer zeros, the same number of zeros, or more zeros than the graph?
6 4. 3 -2x – 5 x<-2 -2 < x < 1 1
4. What is the Horizontal Asymptote of the FUNction 1 - 8 (x + 6) O y = -6 X = -8 O y = -8 O x = 6
05. Graph f(x): S-x + 1; x 2 -2 2х + 3;B х < -2 А. В. С. A. В. С. D. E. not given D.
3/2 (x² – 2)2 Find the length of the graph of f(x) = for 3 < x<7. 3 608 3 608 b) 9. c) O152 d) O304 304 3
7. Graph f(x)=√√3x - 12, state the x and y intercepts if any. x-intercept y-intercept