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Grade 12 Advanced Functions, University Preparation (MHF4U)
B. Trigonometric Functions
16. 12AF.B2.1
16.1 Sine graph: y = sin x
Sine Graph: y = sin x
See exactly how the sine curve is built from the unit circle, learn its amplitude, period, and key points, and practice sketching y = sin x step by step.
What You'll Learn
The graph of y = sin x is a smooth repeating wave built from the y-coordinates of points on the unit circle
Its amplitude is 1, its period is 2 pi, and it passes through the origin at x = 0
Key points at x = 0, pi over 2, pi, 3 pi over 2, and 2 pi let you sketch one full period quickly
Changing the coefficients in y = a sin(bx) stretches or compresses the wave without changing its basic shape
Comparing the sine graph to the cosine and other trig graphs helps you recognize any trig function from its picture
What You'll Practice
1
Finding sine values at key angles using the unit circle
2
Plotting points to graph y = sin x from -2π to 2π
3
Using special triangles to find sine values at angles like π/6
4
Identifying the period and repeated pattern of the sine curve
Why This Matters
Understanding the sine graph is fundamental for modeling periodic phenomena in physics, engineering, and natural sciences. From sound waves to seasonal cycles, sine functions describe repeating patterns you'll encounter throughout advanced math and real-world applications.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Practice exercises
Learning resources
Skills
Sine Function
Unit Circle
Graphing
Periodic Functions
Trigonometry
Coordinates
Special Angles
ON Curriculum Aligned