The cosine of pi (π) is -1.
Here's how you can find that value:
Using the Unit Circle
The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. Angles are measured counterclockwise from the positive x-axis.
- Pi (π) on the Unit Circle: An angle of pi radians (π) corresponds to a point on the unit circle that is directly to the left of the origin. Traveling π radians around the unit circle starts at (1,0) and ends at (-1, 0).
- Coordinates and Cosine: The coordinates of this point are (-1, 0). On the unit circle, the x-coordinate of any point represents the cosine of the corresponding angle, and the y-coordinate represents the sine of the angle.
- Therefore: Since the x-coordinate is -1, cos(π) = -1.
In summary: To find the cosine of pi, visualize the unit circle. Pi radians lands you at the point (-1, 0) on the unit circle. The x-coordinate, which is -1, gives you the cosine value.
