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Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
B. Trigonometric Functions
21. 12AF.B2.7
21.2 Tides and water depth trig problems
Tides and Water Depth Trig Problems
Model rising and falling tide levels with sine and cosine functions, and learn to solve for water depth at any given time.
What You'll Learn
Tide height rises and falls in a repeating pattern that closely matches a sine or cosine curve over time.
A tide model uses amplitude for the swing above and below average, midline for the average depth, and period for the time between high tides.
Writing the equation starts with identifying the maximum depth, minimum depth, and the time it takes to complete one full cycle.
Once the equation is built, plugging in a specific time lets you predict the exact water depth at that moment.
Tide problems are one of several real-world sinusoidal motion problems, alongside Ferris wheels and springs, that share the same modeling steps.
What You'll Practice
1
Writing trigonometric equations from minimum and maximum water depths
2
Calculating water depth at specific times using trig functions
3
Finding time intervals when water depth meets safety requirements
4
Using calculator intersection features to solve real-world constraints
Why This Matters
Understanding tides through trigonometry is essential for marine navigation, coastal engineering, and environmental science. Whether you're planning harbor operations, designing coastal structures, or studying marine ecosystems, predicting water depth accurately ensures safety and informs critical decisions.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Learning resources
Skills
Trigonometric Functions
Negative Cosine
Period and Amplitude
Phase Shift
Real-World Modeling
Graphing Calculator
Time Conversion
ON Curriculum Aligned