cos(-x)
cosx
The function cos(-x) represents the cosine of the opposite of x. In other words, if x is a certain angle, then -x is the angle that is directly opposite to it.
By definition, the cosine function is the ratio of the adjacent side of a right triangle to its hypotenuse. However, since we are dealing with negative angles, we need to adjust our thinking a bit.
If we imagine a unit circle (a circle with a radius of length 1) centered at the origin of a coordinate plane, then cos(-x) will be the x-coordinate of the point on the circle that is -x radians counterclockwise from the positive x-axis (or, equivalently, x radians clockwise from the positive x-axis).
Since the unit circle has symmetry across both the x and y-axes, we know that the x-coordinate of a point that is x radians counterclockwise from the positive x-axis is the same as the x-coordinate of a point that is -x radians counterclockwise from the negative x-axis. Therefore, we can say that:
cos(-x) = cos(x)
In other words, the cosine of a negative angle is equal to the cosine of the positive version of that angle. So, for example, cos(-30 degrees) is equal to cos(30 degrees), which we can evaluate using a unit circle or a trigonometric table to get a value of approximately 0.866.
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