How to Decipher Patterns: A Guide to Mathematical Sequences
A sequence is an ordered list of numbers that follows a rule. In an arithmetic sequence you add the same number each time (2, 5, 8, 11, …), so aₙ = a₁ + (n − 1)d. In a geometric sequence you multiply by the same number each time (3, 6, 12, 24, …), so aₙ […]
Unlocking Trigonometric Secrets: A Comprehensive Guide to Double-Angle and Half-Angle Formulas
TL;DR: Some trig problems look ugly because the angle is doubled or halved, and that is exactly what double-angle and half-angle formulas were built for. The double-angle versions let you rewrite the trig of twice an angle using the trig of the angle itself: sine of 2θ is twice sine θ cosine θ, and cosine […]
