Homework Help is Here – Start Your Trial Now!
Math
Trigonometry
True or False 1]. Changing the period of a sine function changes its domain. Practice Worksheet: Graphs of Trig Functions 3] Changing the phase shift of a tangent function changes its domain. 2] Changing the vertical displacement of a cosecant function changes its range. 4] Changing the vertical stretch of a cotangent function changes its domain.

True or False 1]. Changing the period of a sine function changes its domain. Practice Worksheet: Graphs of Trig Functions 3] Changing the phase shift of a tangent function changes its domain. 2] Changing the vertical displacement of a cosecant function changes its range. 4] Changing the vertical stretch of a cotangent function changes its domain.

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°.
See similar textbooks
icon
Related questions
Question
I need answer for both page and please be specific for all answers thank you
### Graph Analysis Exercise #### Instructions: Identify the features of the graph, then sketch the graph NEATLY using a pencil. #### Problems and Graphs: --- ### 17) \( y = \sin \left( x - \frac{\pi}{2} \right) + 1 \) - **Reflection:** - **Amplitude:** - **Period:** - **Phase shift:** - **Vertical displacement:** **Graph Explanation:** The graph of the sine function is shifted horizontally and vertically. The horizontal shift (phase shift) is to the right by \(\frac{\pi}{2}\) units, and the graph is shifted upwards by 1 unit. Graph: ``` 2 | | 1 | ________ | ——| |— 0 | | -1 | | -2 | | _____|_____|____ -π π/2 2π 3π/2 ``` --- ### 18) \( y = \frac{1}{2} \cos (x + \pi) \) - **Reflection:** - **Amplitude:** - **Period:** - **Phase shift:** - **Vertical displacement:** **Graph Explanation:** The graph of the cosine function is compressed vertically by a factor of \(\frac{1}{2}\) and shifted to the left by \(\pi\) units horizontally. Graph: ``` 2 | 1 | _________ | | -1 | ________| | | -2 | _______|_ | ____|_________ -π π/2 2π ``` --- ### 19) \( y = 3 \sin 2x \) - **Reflection:** - **Amplitude:** - **Period:** - **Phase shift:** - **Vertical displacement:** **Graph Explanation:** This is the graph of the sine function with an amplitude of 3, indicating a vertical stretch. The period is \( \frac{\pi}{2} \) and the function completes its cycle four times as often as the standard sine function. Graph: ``` 3 | __ | / \ 2 |/ \ 1 |\
Transcribed Image Text:### Graph Analysis Exercise #### Instructions: Identify the features of the graph, then sketch the graph NEATLY using a pencil. #### Problems and Graphs: --- ### 17) \( y = \sin \left( x - \frac{\pi}{2} \right) + 1 \) - **Reflection:** - **Amplitude:** - **Period:** - **Phase shift:** - **Vertical displacement:** **Graph Explanation:** The graph of the sine function is shifted horizontally and vertically. The horizontal shift (phase shift) is to the right by \(\frac{\pi}{2}\) units, and the graph is shifted upwards by 1 unit. Graph: ``` 2 | | 1 | ________ | ——| |— 0 | | -1 | | -2 | | _____|_____|____ -π π/2 2π 3π/2 ``` --- ### 18) \( y = \frac{1}{2} \cos (x + \pi) \) - **Reflection:** - **Amplitude:** - **Period:** - **Phase shift:** - **Vertical displacement:** **Graph Explanation:** The graph of the cosine function is compressed vertically by a factor of \(\frac{1}{2}\) and shifted to the left by \(\pi\) units horizontally. Graph: ``` 2 | 1 | _________ | | -1 | ________| | | -2 | _______|_ | ____|_________ -π π/2 2π ``` --- ### 19) \( y = 3 \sin 2x \) - **Reflection:** - **Amplitude:** - **Period:** - **Phase shift:** - **Vertical displacement:** **Graph Explanation:** This is the graph of the sine function with an amplitude of 3, indicating a vertical stretch. The period is \( \frac{\pi}{2} \) and the function completes its cycle four times as often as the standard sine function. Graph: ``` 3 | __ | / \ 2 |/ \ 1 |\
**Practice Worksheet: Graphs of Trig Functions** --- ### True or False 1. _______ Changing the period of a sine function changes its domain. 2. _______ Changing the vertical displacement of a cosecant function changes its range. 3. _______ Changing the phase shift of a tangent function changes its domain. 4. _______ Changing the vertical stretch of a cotangent function changes its domain. --- ### Analyze the equation to determine the features of the graph of each function. 5. \( y = 3 \sin 2x - 4 \) - **amplitude:** - **period:** - **phase shift:** - **vertical displacement:** - **reflection:** 6. \( y = -4 \cos \left( \frac{1}{3} x \right) \) - **amplitude:** - **period:** - **phase shift:** - **vertical displacement:** - **reflection:** 7. \( y = 5 \csc \left( x - \frac{\pi}{3} \right) + 2 \) - **vertical stretch/shrink:** - **phase shift:** - **period:** - **vertical displacement:** - **reflection:** 8. \( y = 7 \sec \left( 4 \left( x + \frac{\pi}{4} \right) \right) - 1 \) - **vertical stretch/shrink:** - **phase shift:** - **period:** - **vertical displacement:** - **reflection:** 9. \( y = 4 \tan \left( \frac{2}{3} x \right) + 6 \) - **vertical stretch/shrink:** - **phase shift:** - **period:** - **vertical displacement:** - **reflection:** 10. \( y = \frac{1}{2} \cot (-x) + 1 \) - **vertical stretch/shrink:** - **phase shift:** - **period:** - **vertical displacement:** - **reflection:** --- ### Fill in the blanks to complete the table. | Function | Vertical Stretch/Shrink | Period | Phase Shift | Vertical Displacement | Equation | |----------|--------------------------
Transcribed Image Text:**Practice Worksheet: Graphs of Trig Functions** --- ### True or False 1. _______ Changing the period of a sine function changes its domain. 2. _______ Changing the vertical displacement of a cosecant function changes its range. 3. _______ Changing the phase shift of a tangent function changes its domain. 4. _______ Changing the vertical stretch of a cotangent function changes its domain. --- ### Analyze the equation to determine the features of the graph of each function. 5. \( y = 3 \sin 2x - 4 \) - **amplitude:** - **period:** - **phase shift:** - **vertical displacement:** - **reflection:** 6. \( y = -4 \cos \left( \frac{1}{3} x \right) \) - **amplitude:** - **period:** - **phase shift:** - **vertical displacement:** - **reflection:** 7. \( y = 5 \csc \left( x - \frac{\pi}{3} \right) + 2 \) - **vertical stretch/shrink:** - **phase shift:** - **period:** - **vertical displacement:** - **reflection:** 8. \( y = 7 \sec \left( 4 \left( x + \frac{\pi}{4} \right) \right) - 1 \) - **vertical stretch/shrink:** - **phase shift:** - **period:** - **vertical displacement:** - **reflection:** 9. \( y = 4 \tan \left( \frac{2}{3} x \right) + 6 \) - **vertical stretch/shrink:** - **phase shift:** - **period:** - **vertical displacement:** - **reflection:** 10. \( y = \frac{1}{2} \cot (-x) + 1 \) - **vertical stretch/shrink:** - **phase shift:** - **period:** - **vertical displacement:** - **reflection:** --- ### Fill in the blanks to complete the table. | Function | Vertical Stretch/Shrink | Period | Phase Shift | Vertical Displacement | Equation | |----------|--------------------------
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry
Algebra and Trigonometry
Trigonometry
ISBN:
9781938168376
Author:
Jay Abramson
Publisher:
OpenStax
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS