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Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
B. Trigonometric Functions
16. 12AF.B2.1
16.2 Cosine graph: y = cos x
Cosine Graph: y = cos x
See how the cosine graph is built from the unit circle, learn its amplitude, period, and key points, and practice graphing transformations of cosine.
What You'll Learn
The graph of y = cos x is a smooth wave that starts at its maximum value of 1 when x = 0
It repeats every 2 pi radians (360 degrees), which is called its period
Its amplitude is 1, meaning the graph oscillates between y = 1 and y = negative 1
Cosine is an even function, so its graph is symmetric about the y-axis
Changing A, B, and D in y = A cos(Bx) + D stretches, compresses, or shifts the basic cosine graph
What You'll Practice
1
Finding cosine values at standard angles using unit circle coordinates
2
Plotting cosine function points in both positive and negative directions
3
Connecting plotted points to sketch the complete cosine curve
4
Identifying period and repeating patterns in the cosine graph
Why This Matters
Understanding the cosine graph is essential for modeling periodic phenomena like sound waves, alternating currents, and oscillations in physics and engineering. This foundation prepares you for advanced trigonometry, calculus, and real-world applications in science and technology.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Learning resources
Skills
Cosine Function
Unit Circle
Trigonometric Graphs
Periodic Functions
Angle Measures
Coordinate System
Function Plotting
ON Curriculum Aligned