The value of cos pi is -1.
Understanding Cosine of Pi
The question asks for the value of the cosine function at the angle π (pi). Pi (π) radians is equivalent to 180 degrees. Therefore, cos pi is the same as cos 180°.
Why is cos pi equal to -1?
- Unit Circle: The cosine of an angle can be visualized using the unit circle, which is a circle with a radius of 1 centered at the origin of a coordinate plane. An angle is measured counter-clockwise from the positive x-axis.
- Coordinates: The x-coordinate of the point where the terminal side of the angle intersects the unit circle represents the cosine of the angle.
- 180 Degrees: For 180 degrees or π radians, the terminal side points directly along the negative x-axis.
- Intersection: The point of intersection on the unit circle is (-1, 0). Thus the x-coordinate, which represents the cosine, is -1.
Summary
| Function | Angle (Radians) | Angle (Degrees) | Value |
|---|---|---|---|
| cos | π | 180° | -1 |
Therefore, cos π = -1. This is a fundamental trigonometric value.
