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

Writing equations using positive and negative sine functions for the same periodic curve

Writing equations using positive and negative cosine functions for the same periodic curve

Finding period by calculating distances between maximum and minimum points

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:

Sine graph: y = sin x Cosine graph: y = cos x Graphing transformations of trigonometric functions

This Unit Includes

3 Video lessons

Skills

Trigonometric Functions

Amplitude

Period

Phase Shift

Graph Analysis

Sine and Cosine

Function Modeling

OH Curriculum Aligned