Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
4. Graphing Trigonometric Functions
Graphs of the Sine and Cosine Functions
8:38 minutes
Problem 35d
Textbook Question
Textbook QuestionIn Exercises 35–42, determine the amplitude and period of each function. Then graph one period of the function. y = cos 2x
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Amplitude
Amplitude refers to the maximum height of a wave from its central axis. In trigonometric functions like cosine, it indicates how far the function reaches above and below its midline. For the function y = cos(2x), the amplitude is 1, as the cosine function oscillates between -1 and 1.
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Period
The period of a trigonometric function is the length of one complete cycle of the wave. For the cosine function, the standard period is 2π. However, when the function is modified, such as in y = cos(2x), the period is adjusted by the coefficient of x, resulting in a new period of π, meaning the function completes one full cycle in that interval.
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Graphing Trigonometric Functions
Graphing trigonometric functions involves plotting the values of the function over a specified interval. For y = cos(2x), one period can be graphed from 0 to π, showing the characteristic wave shape. Understanding the amplitude and period is crucial for accurately representing the function's behavior on a graph.
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