Chapter 32.1
Graphing transformations of trigonometric functions
What You'll Learn
Identify how parameters A, B, C, and D transform trigonometric graphs
Determine amplitude, period, phase shift, and vertical displacement from equations
Graph transformed sine, cosine, secant, and tangent functions for multiple periods
Find domain and range of transformed trigonometric functions
Locate vertical asymptotes in secant and tangent transformations
What You'll Practice
1
Graphing sine and cosine transformations using the five-point method
2
Drawing secant graphs by first sketching cosine then flipping segments
3
Graphing negative trigonometric functions with reflections across the x-axis
4
Finding equations of vertical asymptotes for tangent and secant functions
5
Calculating period, amplitude, and shifts from transformed trig equations
Why This Matters
Mastering transformations of trigonometric functions is essential for modeling real-world periodic phenomena like sound waves, tides, and seasonal patterns. These skills are foundational for calculus, physics, and engineering courses where you'll analyze oscillating systems and wave behavior.
Before You Start — Make Sure You Can:
This Unit Includes
4 Video lessons
Practice exercises
Skills
Trigonometric Graphs
Transformations
Amplitude
Period
Phase Shift
Vertical Displacement
Asymptotes
Domain and Range
OH Curriculum Aligned
