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Chapter 15.8
Determining trigonometric functions given their graphs
What You'll Learn
Identify which trigonometric function (sine, cosine, negative sine, negative cosine) best models a given graph
Calculate amplitude, period, phase shift, and vertical shift from graph features
Determine the equation parameters A, B, C, and D from maximum, minimum, and middle line values
Extract trigonometric curves by matching graph shape to function type
Apply the period formula to solve for the B value in trigonometric equations
What You'll Practice
1
Writing equations using positive and negative sine functions for the same periodic curve
2
Writing equations using positive and negative cosine functions for the same periodic curve
3
Finding period by calculating distances between maximum and minimum points
4
Determining phase shift from graph starting points with smallest shift values
Why This Matters
Reading and writing trigonometric equations from graphs is essential for modeling periodic phenomena like sound waves, tides, and oscillations. This skill bridges visual graph interpretation with algebraic representation, preparing you for advanced applications in physics, engineering, and calculus.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Skills
Trigonometric Functions
Amplitude
Period
Phase Shift
Graph Analysis
Sine and Cosine
Function Modeling
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