cos (-x)
In mathematics, the function “cos” refers to the cosine of an angle
In mathematics, the function “cos” refers to the cosine of an angle. The cosine function is defined for all real numbers and it gives the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. However, when dealing with angles, we often use the unit circle to define the cosine function.
The cosine function can take any angle, whether positive or negative. In the case of cos(-x), we have a negative angle. This means that we are looking for the cosine of an angle that is formed by a rotation in the clockwise direction.
To understand the value of cos(-x), we can utilize the concept of periodicity. The cosine function has a period of 360 degrees or 2π radians, which means it repeats itself after every interval of 360 degrees or 2π radians. Therefore, for any angle x, if we subtract a full rotation of 360 degrees or 2π radians, we end up in the same position on the unit circle, since the cosine function has the same value for angles that differ by a multiple of 360 degrees.
So, cos(-x) can be rewritten as cos(-x + 360 degrees) or cos(-x + 2π radians). Now we can see that -x + 360 degrees or -x + 2π radians is equivalent to an angle formed by rotating x in the counterclockwise direction by 360 degrees or 2π radians. As a result, the cosine of this angle would be the same as the cosine of x.
In other words, cos(-x) is equal to cos(x). Therefore, the cosine of a negative angle is equal to the cosine of its positive counterpart.
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