○ The Unit Circle ○

  • This video explains how to use the unit circle to define the trigonometric ratios of sine, cosine, and tangent for all real numbers.

  • This video explains how for acute angles (in Quadrant I), the two different definitions of the trigonometric values (SOH CAH TOA: Sin=Opposite/Hypotenuse, Cosine=Adjacent/Hypotenuse, and Tan=Opposite/Adjacent) and the unit circle definition result in the same values.

〰️ Orders of Magnitude 〰️

  • This video describes what is meant by an order of magnitude, in which situations they are used, and how to estimate sizes in terms of order of magnitude.

  • This video applies orders of magnitude to a practical example: finding the height of Mount Everest.

  • This video applies orders of magnitude to a practical example: finding the Earth's diameter.

🔁 Motion Problems 🔁

  • This video defines the difference between displacement and distance. The definite integral of a velocity function gives us the displacement. To find the actual distance traveled, we need to use the speed function, which is the absolute value of the velocity.

  • This video explains the relationship between position, velocity, and acceleration. If position is given by a function p(t), then the velocity, v(t), is the first derivative of that function, and the acceleration, a(t) is the second derivative. This concept is covered in our mathematics and physics courses.

  • This study guide defines: distance, speed and acceleration, force and pressure, work, energy, conservation of energy (potential and kinetic energy) and the equivalence of work and energy.

  • This video provides a basic introduction to pressure. Pressure is defined as force per unit area. 1 Pascal equals 1 Newton of force per square meter of area. It also discusses the inverse relationship between elevation and atmospheric pressure. As the elevation increases, the atmospheric pressure decreases and the boiling point of water decreases.