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

Tuesday, February 6, 2018

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.

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.