Find the period and graph the function. y = - tan x period = II x rad 3
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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![**Find the Period and Graph the Function**
Given Function:
\[ y = -\frac{1}{3} \tan x \]
**Period Calculation:**
The period is given as \(\pi\) radians.
**Graphs:**
1. **Upper Left Graph:**
- This graph shows the function \( y = -\frac{1}{3} \tan x \) with vertical asymptotes at \( x = -\frac{\pi}{2} \), \( x = \frac{\pi}{2} \), \( x = \frac{3\pi}{2} \).
- The red curve indicates the transformation of the tangent function, stretched vertically by a factor of \(-\frac{1}{3}\).
- The curve decreases from left to right, passing through the origin.
2. **Upper Right Graph:**
- Displays vertical asymptotes at \( x = -\frac{3\pi}{2} \), \( x = -\frac{\pi}{2} \), \( x = \frac{\pi}{2} \).
- Similar transformation as the upper left graph but shifted horizontally.
- The curve decreases and passes through \( y = 0 \) at \( x = 0 \).
3. **Lower Left Graph:**
- Asymptotes are positioned similar to the upper left graph.
- The curve’s behavior remains consistent, demonstrating periodicity.
4. **Lower Right Graph:**
- Shows asymptotes at \( x = -\pi \), \( x = \pi \), and \( x = 3\pi \).
- The behavior follows the pattern described in previous graphs.
Each graph represents a segment of the periodic function, illustrating the consistent interval pattern \(\pi\) across the x-axis. The transformation by \(-\frac{1}{3}\) affects the slope and symmetry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc223299-9733-49e9-a81c-da383b176e19%2Fe82f6e0f-2be1-4e57-9ba5-7465f49b7506%2F9hzqozn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the Period and Graph the Function**
Given Function:
\[ y = -\frac{1}{3} \tan x \]
**Period Calculation:**
The period is given as \(\pi\) radians.
**Graphs:**
1. **Upper Left Graph:**
- This graph shows the function \( y = -\frac{1}{3} \tan x \) with vertical asymptotes at \( x = -\frac{\pi}{2} \), \( x = \frac{\pi}{2} \), \( x = \frac{3\pi}{2} \).
- The red curve indicates the transformation of the tangent function, stretched vertically by a factor of \(-\frac{1}{3}\).
- The curve decreases from left to right, passing through the origin.
2. **Upper Right Graph:**
- Displays vertical asymptotes at \( x = -\frac{3\pi}{2} \), \( x = -\frac{\pi}{2} \), \( x = \frac{\pi}{2} \).
- Similar transformation as the upper left graph but shifted horizontally.
- The curve decreases and passes through \( y = 0 \) at \( x = 0 \).
3. **Lower Left Graph:**
- Asymptotes are positioned similar to the upper left graph.
- The curve’s behavior remains consistent, demonstrating periodicity.
4. **Lower Right Graph:**
- Shows asymptotes at \( x = -\pi \), \( x = \pi \), and \( x = 3\pi \).
- The behavior follows the pattern described in previous graphs.
Each graph represents a segment of the periodic function, illustrating the consistent interval pattern \(\pi\) across the x-axis. The transformation by \(-\frac{1}{3}\) affects the slope and symmetry.
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