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Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
B. Trigonometric Functions
20. 12AF.B2.6
20.1 Determining trigonometric functions given their graphs
Determining Trig Functions Given Their Graphs
A step-by-step method for turning a sine or cosine curve into its equation by reading amplitude, period, midline, and shift directly off the graph.
What You'll Learn
Reading a trig graph means identifying four features: amplitude, midline, period, and phase shift, plus whether the curve is reflected.
Amplitude is the distance from the midline to a maximum or minimum, and it becomes the coefficient in front of sine or cosine.
The period tells you the value of \(B\) using the relationship period equals two pi divided by \(B\).
A graph that starts at its midline going down, instead of up, indicates a reflection and a negative leading coefficient.
The same curve can often be written correctly as either a shifted sine equation or a shifted cosine equation.
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
Learning resources
Skills
Trigonometric Functions
Amplitude
Period
Phase Shift
Graph Analysis
Sine and Cosine
Function Modeling
ON Curriculum Aligned