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Integrated Math II
27. CC.HSF.TF.B.5
27.1 Graphing transformations of trigonometric functions
Graphing Transformations of Trigonometric Functions
See exactly how amplitude, period, phase shift, and vertical shift reshape and reposition a trig graph, with worked examples and visuals.
What You'll Learn
A transformed trig function has the form y equals A times sine or cosine of B times the quantity x minus C, plus D
The amplitude is the absolute value of A and it stretches or compresses the graph vertically
The period equals two pi divided by the absolute value of B and it stretches or compresses the graph horizontally
The phase shift equals C and it slides the graph left or right, while D slides it up or down
Working through each parameter one at a time turns a complicated-looking equation into an easy sketch
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
Learning resources
Skills
Trigonometric Graphs
Transformations
Amplitude
Period
Phase Shift
Vertical Displacement
Asymptotes
Domain and Range
OH Curriculum Aligned