Part 3/5:
Thus, the graph confirms that sine is indeed an odd function. By visually inspecting it, we grasp the essential property of the sine function, providing a clear foundation for the trigonometric identity for negative angles.
Understanding Cosine Through Reflection
On the other hand, the cosine function defines the x-coordinate of points on the unit circle. Notably, when we look at a negative angle -θ, the x-coordinate remains unchanged. This symmetry can be easily observed as the graph of cosine reflects across the y-axis. Therefore, we can confidently state that:
cos(-θ) = cos(θ)
This property showcases that cosine is an even function, reinforcing our understanding of its behavior in relation to negative angles.