What is the value of cos(-π)?

The value of cos(-π) can be determined using the properties of the cosine function and its relationship to angles on the unit circle. To break this down, let's first recall some key concepts about the cosine function.

Understanding Cosine and the Unit Circle

The cosine function is periodic and even, which means that cos(-θ = cos(θ). This property is crucial when evaluating cosine for negative angles. In our case, we want to find cos(-π).

Evaluating cos(-π)

Since cosine is an even function, we can simplify our expression:

• cos(-π) = cos(π)

Now, let's find cos(π). On the unit circle, the angle π radians corresponds to the point (-1, 0). The cosine of an angle is defined as the x-coordinate of the corresponding point on the unit circle.

Finding the Value

At the angle π, the coordinates are (-1, 0), so:

• cos(π) = -1

Therefore, we can conclude:

• cos(-π) = cos(π) = -1

Final Thoughts

In summary, the value of cos(-π) is -1. This result highlights the symmetry of the cosine function and its behavior on the unit circle. Understanding these properties not only helps in solving similar problems but also deepens your grasp of trigonometric functions as a whole.