The value of sec π is -1.
Understanding Secant
Secant (sec) is a trigonometric function that is the reciprocal of cosine (cos). In other words:
- sec θ = 1 / cos θ
Finding sec π
- The cosine of π (cos π) is -1.
- Therefore, the secant of π (sec π) is 1 / -1, which equals -1.
Visual Representation
You can visualize this on the unit circle:
- π radians corresponds to 180 degrees, which lies on the negative x-axis.
- The x-coordinate of this point on the unit circle represents the cosine value, which is -1.
- Since secant is the reciprocal of cosine, sec π is 1 / -1, which is -1.
In Summary
The value of sec π is -1. This can be found by understanding the relationship between secant and cosine and by using the unit circle to visualize the cosine value at π.
