Where in the Sphere?

Pre-Calculus introduces topics that become crucial to the continuum of topics of higher level math such as Calculus, Linear Algebra, Differential Equations, and beyond. This section also becomes the most difficult to learn and practice due to the applications of the topics and where to see it across different fields in STEM.

Pre-Calculus can be found within the Quantum Sciences which applies Trigonometric Functions (sine, cosine, tangent), Unit Circle (Degrees, Radians, Coordinates), and polar coordinates which could extend into the 3 Dimensional space. The Quantum Bloch Sphere measures the result of a quantum bit (qubit) which behaves differently from a classical binary bit. The Bloch Sphere is an example of what the probability of a qubit could be and is not an actual model of quantum measurement, so this final assessment will lead with students predicting a qubit probability using 3 Dimensional Spherical coordinates.

This lesson series is designed to take the Unit Circle approach from a 2 Dimensional space and introduce students to the same annotation through polar coordinates. Once students become familiar with polar coordinates, then students will be exposed to a 3 Dimensional space through the use of polar coordinates that include Cylindrical Coordinates then use Spherical Coordinates.