Understanding Cos(-x) in Trigonometry | The Concept and Application of Negative Angles in the Cosine Function

cos(-x)

The cosine function is a mathematical function that associates an angle measurement with the ratio of the length of the adjacent side of a right triangle to the length of the hypotenuse

The cosine function is a mathematical function that associates an angle measurement with the ratio of the length of the adjacent side of a right triangle to the length of the hypotenuse. It is denoted by “cos” and is defined for all real numbers.

Now, let’s understand the concept of cos(-x). In trigonometry, negative angles can be thought of as rotating clockwise rather than counterclockwise. The cosine of a negative angle can be determined by taking the cosine of the positive value of that angle.

Using the unit circle as a reference, the cosine function is represented by the x-coordinate of a point on the circle. When considering an angle of -x, it means we are moving clockwise by an angle of x from the positive x-axis.

Since the cosine function is an even function, the cosine of -x will be the same as the cosine of x. In other words, cos(-x) = cos(x).

To summarize, when you find the cosine of a negative angle, you can simply take the cosine of the positive value of that angle. The resulting value will be the same.

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