Tides and Seasonal Modelling

Key idea

Sinusoidal models of periodic data.

In depth

Periodic phenomena are modelled with y = A sin(B(x − h)) + k. Fit the period from observed data, the midline from the average, and the amplitude from the half range.

Worked example

High tide 4.0 m, low tide 1.0 m, 12.4 hours apart in cycle: A = 1.5, k = 2.5, B = 2π/12.4.

Real-world uses

• Predicting high and low tides for ports and sunlight hours through the year

Common mistake

Using the time between high and low tide as the period; it is only half.

How to learn this

1. Read the key idea and say it in your own words.
2. Work through the worked example, then try a similar problem.
3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

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Related advanced topics in Trigonometry

• Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
• Phase Shift – Horizontal translation of a wave.
• Vertical Shift and Midline – Moves the wave up or down.
• General Sinusoid – Combine amplitude, period, phase and shift.
• Graphs of Reciprocal Trig Functions – Secant, cosecant and cotangent graphs.
• Pythagorean Identity – The key identity from the unit circle.