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Name Date Modeling with Trigonometric Functions 9.6 For use with Exploration 9.6 Essential Question What are the characteristics of the real life problems that can be modeled by trigonometric functions?

How to fill out modeling with trigonometric functions

How to fill out modeling with trigonometric functions?

1. Determine the problem or scenario that you want to model. This could be anything from motion, waves, or periodic patterns.
2. Understand the basic trigonometric functions such as sine, cosine, and tangent. These functions relate the angles of a right triangle to the ratios of the triangle's side lengths.
3. Identify the variables in your problem that can be represented using trigonometric functions. For example, if you are modeling the height of a person on a Ferris wheel, the angle of rotation could be represented by a trigonometric function.
4. Use the appropriate trigonometric function to express the relationship between the variables. This may involve adjusting the amplitude, period, or phase shift of the basic function to fit your specific scenario.
5. Plot the graph of your trigonometric function using appropriate scales for the variables involved. This will help visualize the pattern or relationship you are modeling.
6. Analyze the graph to gain insights into the behavior of the variables in your problem. This may involve determining maximum or minimum values, intervals of increase or decrease, or any other relevant information.
7. Test your model by plugging in different values for the variables and compare the results to real-world observations or data. Adjust the model if necessary to improve its accuracy.

Who needs modeling with trigonometric functions?

1. Engineers and physicists often need to use trigonometric functions to model and understand various phenomena in the physical world. This could include analyzing the motion of objects, studying vibrations and waves, or predicting periodic behavior in electrical circuits.
2. Architects and designers might use trigonometric functions to model and design structures with specific angles, shapes, or movements. This could be seen in the design of bridges, buildings, or even animated objects in computer graphics.
3. Mathematicians and researchers in mathematics often explore and develop new models using trigonometric functions. They may study the mathematical properties of these functions, discover new relationships, or apply them in other areas of mathematics such as calculus or number theory.

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