Advanced Trigonometric Functions and Graph Writing
This section delves into the techniques for writing equations from graphs and understanding more complex trigonometric functions including tangent, cotangent, secant, and cosecant.
Definition: The process of writing equations involves finding amplitude (A), vertical shift (D), period factor (B), and phase shift (C).
Example: For finding amplitude: Calculate half the distance between maximum and minimum points of the graph.
Highlight: Special characteristics of advanced functions:
- Tangent: Period π, asymptotes at x = π/2 + πk
- Cotangent: Period π, asymptotes at x = πk
- Secant: Period 2π, range (-∞,-1] ∪ [1,∞)
- Cosecant: Period 2π, range (-∞,-1] ∪ [1,∞)
Vocabulary: Asymptotes are lines that a graph approaches but never touches, crucial in understanding tangent, cotangent, secant, and cosecant functions.