Understanding the Cosine Function | Exploring cos(-x) and its Relationship with cos(x) on the Unit Circle

cos(-x)

The cosine function, denoted as cos(x), is a trigonometric function that represents the ratio of the adjacent side to the hypotenuse in a right triangle

The cosine function, denoted as cos(x), is a trigonometric function that represents the ratio of the adjacent side to the hypotenuse in a right triangle. It can also be defined using the unit circle.

Now, let’s consider cos(-x). When the argument of the cosine function is negative, like in this case with -x, it means we are looking for the cosine of an angle in the opposite direction from the positive x-axis.

To understand cos(-x) better, let’s visualize it on the unit circle. The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in a coordinate plane.

Starting from the positive x-axis, moving counterclockwise, the cosine function gives us the x-coordinate of the point on the unit circle corresponding to the angle measured in radians. Since cosine is an even function, the value of cos(-x) is the same as cos(x), meaning the x-coordinate of the point located on the unit circle with an angle of -x is the same as the x-coordinate of the point with an angle of x.

In simple terms, cos(-x) = cos(x). This result is because the cosine values repeat themselves as we move around the unit circle in either direction.

To summarize, cos(-x) is equal to cos(x) since the cosine function yields the same value for positive and negative angles.

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