Calc 1, Lec 6B: Logarithm Proof, Graphs of Logs, Cosine & Sine Unit Circle Def, Sinusoidal Functions

(0:00) Proof of the product to sum property of logarithms.
(9:14) Visualizing this property as an equivalence between a horizontal compressions toward the y axis with an upward vertical translation away from the x axis.
(11:26) Calculus related properties of logarithmic graphs, especially when b is greater than one (continuity, smoothness, increasing, concave down, unbounded (no horizontal asymptote), and vertical asymptote at x = 0).
(16:17) Unit circle definition of the trigonometric functions (cosine, sine, and tangent), with the angle measured in radians (based on an equal arc length along the unit circle). Special values briefly discussed.
(26:08) General sinusoidal functions (to model "pure" oscillatory behavior). Discuss amplitude, period (wavelength), frequency, average value (midline), and horizontal shift (related to the "phase angle").