# Measuring Your World: DP Update Part 1

**Due Date:** Monday, February 26 before 11:59pm**Late Deadline:** Monday, March 5 before 11:59pm**Mode:** You must e-mail Dr. Drew a link to your "Measuring Your World" DP page**Revisions:** You may submit a revision of your work for **at most one more grade point**

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:

- Sine
- Cosine
- Tangent
- ArcSine
- ArcCosine
- ArcTangent
- Law of Sines
- Law of Cosines

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

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

Remember: your goal is not to teach someone what you have learned; the goal is to explain what you have learned and how it relates to solving measurement problems. If you are in doubt about too much or too little detail, please get started and then ask me to review your work before you get to far.