Properties of $y = \cos x$ and Its Graph
🎯 Learning Objectives
- Understand the shape and key features of the cosine function graph
- Identify amplitude, period, domain, range, and symmetry
- Locate intercepts, maximum, and minimum points
- Compare cosine to sine and understand transformations
📐 Definition of the Cosine Function
The cosine function $y = \cos x$ assigns to each real number $x$ (an angle measured in radians) the $x$-coordinate of the corresponding point on the unit circle.
Formal Definition
For any angle $x$ (in radians), if the terminal side of the angle intersects the unit circle at point $(a, b)$, then:
$$\cos x = a$$
This means cosine gives us the horizontal coordinate on the unit circle.