Robotics 101
This project was extremely challenging. We used all of the concepts we have learned throughout the year and had to apply it to this one problem. Of course it was a story problem of sorts with pictures to help you through it. There were a lot of questions and having the ability to consult with my peers and teacher was extremely helpful. The project was meant to show how trigonometry is used in real world applications. This particular application was about a robot being able to pick up things and move them. This required much higher critical thinking than any other project I have attempted.
Skills and Objectives
- Define using the unit circle, graph and use all trigonometric functions of any angle. Convert between radian and degree measure. Calculate arc length, and area of a sector in a given circle.
- Graph transformations of the sine and cosine functions (involving changes in amplitude, period, midline and phase changes) and explain the relationship between constraints in the formula and transformed graph.
- Graph transformations of tangent functions
- Prove trigonometric identities and derive some of the basic ones. Know the fundamental identities.
- Find a sinusoidal function to model a given data set or situation and explain how the parameters of the model relate to the data set or situation.
- Know the basic properties of the inverse trigonometric functions: sin-1x, cos-1x, tan-1x, including their domains and ranges. Recognize their graphs.
- Know basic trigonometric identities for sine cosine and tangent ( Fundamental, sum and difference, co functions, double and half angle formulas)
- Solve trigonometric equation using basic identities and inverse trigonometric functions
- Prove the addition and subtraction formula for sine, cosine, and tangent and use them to solve problems.
- Prove trigonometric identities and derive some of the basic ones ( double angle formulas from sum and difference formulas, half angles formula from double angle formula)
- Real world applications of problems involving trigonometry such as the laws of sine and cosine.
Justification
This project was extremely difficult and required all of my mathematical skill to conquer it. The problem was difficult but with the help from others I was able to accomplish this daunting task. This has been a great year for learning math for me I have learned more in one year than I have in all my others years of math by far. For these reasons I have included this in my portfolio.
robotics_101.pdf | |
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