Amplitude, Period And Trigonometric Graphs
Overview
Stretching and shifting the basic sine, cosine and tangent graphs produces a whole family of curves. Two numbers control most of it: the amplitude (how tall the wave is) and the period (how often it repeats).
In this lesson you will understand and use the amplitude and period of a trigonometric function, and draw and use the graphs of \(y = a \sin bx + c\), \(y = a \cos bx + c\) and \(y = a \tan bx + c\).
Objectives
- Understand and use the amplitude and period of a trigonometric function, including the relationship between graphs of related trigonometric functions.
- Draw and use the graphs of y = a sin bx + c, y = a cos bx + c and y = a tan bx + c.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Amplitude, Period And Trigonometric Graphs. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- For y = 3 sin 2x, the amplitude is: A. 2 B. 3 C. 6 D. 180 Answer: B
- For y = 3 sin 2x, the period is: A. 90° B. 180° C. 360° D. 720° Answer: B
- In y = a sin bx + c, the period is: A. a B. 360/b C. b/360 D. c Answer: B
- In y = a sin bx + c, the constant c: A. changes amplitude B. changes period C. shifts the graph vertically D. has no effect Answer: C
- The amplitude of y = 5 cos x is: A. 1 B. 5 C. 10 D. 360 Answer: B
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