The cosine of π (pi) is found on the unit circle by identifying the x-coordinate of the point where the angle π intersects the circle, which is -1.
Understanding the Unit Circle
The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the coordinate plane. Angles are measured counterclockwise from the positive x-axis.
Locating π on the Unit Circle
An angle of π radians (180 degrees) corresponds to a point on the unit circle that lies directly on the negative x-axis.
Determining the Cosine Value
- Cosine corresponds to the x-coordinate: On the unit circle, the cosine of an angle is represented by the x-coordinate of the point where the terminal side of the angle intersects the circle.
- Coordinates at π: At the angle π, the coordinates of the point on the unit circle are (-1, 0).
- Therefore: Since the x-coordinate at π is -1, cos(π) = -1.
In summary, visualizing the unit circle and remembering that cosine corresponds to the x-coordinate allows you to quickly determine that cos(π) = -1.
