Graph the function. 18) y = tan 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°.
Related questions
Question
![**Title: Graph the Function**
**Problem 18:**
\[ y = \frac{1}{4} \tan 2x \]
**Graph Explanation:**
- The x-axis and y-axis intersect at the origin (0,0).
- The graph is set up with tick marks along both axes to indicate scale.
- The function \( y = \frac{1}{4} \tan 2x \) is a transformation of the basic tangent function.
- The coefficient \(\frac{1}{4}\) vertically compresses the graph, affecting the amplitude of the output values.
- The \(2x\) inside the tangent function indicates a horizontal compression, which affects the period of the tangent graph. The period of \(\tan 2x\) is \(\pi\), as opposed to the standard period of \(\pi\) for \(\tan x\).
- The graph will have vertical asymptotes at \(x = \pm \frac{\pi}{4}, \pm \frac{3\pi}{4}, \) and so on, repeating every \(\frac{\pi}{2}\).
**Note:**
- The tangent function is periodic and has vertical asymptotes where the function value approaches infinity.
- The \(\frac{1}{4}\) factor affects how steep the graph appears, making the increase less steep compared to \(\tan 2x\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f9e96de-8215-4532-a7d0-6f1fdf87f241%2F7333f43a-36a2-4403-9fc1-e5b21850b2c0%2F70jkelp_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Graph the Function**
**Problem 18:**
\[ y = \frac{1}{4} \tan 2x \]
**Graph Explanation:**
- The x-axis and y-axis intersect at the origin (0,0).
- The graph is set up with tick marks along both axes to indicate scale.
- The function \( y = \frac{1}{4} \tan 2x \) is a transformation of the basic tangent function.
- The coefficient \(\frac{1}{4}\) vertically compresses the graph, affecting the amplitude of the output values.
- The \(2x\) inside the tangent function indicates a horizontal compression, which affects the period of the tangent graph. The period of \(\tan 2x\) is \(\pi\), as opposed to the standard period of \(\pi\) for \(\tan x\).
- The graph will have vertical asymptotes at \(x = \pm \frac{\pi}{4}, \pm \frac{3\pi}{4}, \) and so on, repeating every \(\frac{\pi}{2}\).
**Note:**
- The tangent function is periodic and has vertical asymptotes where the function value approaches infinity.
- The \(\frac{1}{4}\) factor affects how steep the graph appears, making the increase less steep compared to \(\tan 2x\).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning