Feb 6: Head Start: DP Update for Measuring Your World

For the "Measuring Your World" project, you will be doing another DP update. A big part of this update will be explaining how you learned about 8 trigonometric formulas:

  1. Sine
  2. Cosine
  3. Tangent
  4. ArcSine
  5. ArcCosine
  6. ArcTangent
  7. Law of Sines
  8. Law of Cosines

You will basically write a narrative that summarizes the major steps in your learning. Those steps are:

  1. Proving the Pythagorean Theorem
  2. Using the Pythagorean Theorem to derive the Distance Formula
  3. Using the Distance Formula to derive the equation of a circle centered at the origin of a Cartesian coordinate plane
  4. Defining the Unit Circle
  5. Finding points on the unit circle (at 30 degrees, 45 degrees and 60 degrees)
  6. Using the symmetry of a circle to find the remaining points on the unit circle
  7. Using the unit circle to define sine and cosine (of the angle theta)
  8. Defining the tangent function
  9. Using similarity and proportions to derive the general trigonometric functions (sine, cosine and tangent)
  10. Using the unit circle to define the arcSine, arcCosine and arcTangent functions
  11. Using the Mount Everest problem to discover the Law of Sines ("taking apart")
  12. Deriving the Law of Sines
  13. Deriving the Law of Cosines

In your narrative, you should emphasize the importance (that is, the application) of each of the 8 functions: in other words, you must explain when they are used to solve problems related to the most basic of 2-dimensional shapes: the triangle.

This "announcement" will soon become an "assignment"; that is, this part of your DP will be graded separately from the rest of the project work that will be posted to your DP.