Understanding the Cosine Function: Exploring the Identity and Symmetry of cos(-x)

cos(-x)

The cosine function, written as cos(x), is a trigonometric function that relates the angle x to the ratio of the length of the side adjacent to the angle x to the hypotenuse in a right triangle

The cosine function, written as cos(x), is a trigonometric function that relates the angle x to the ratio of the length of the side adjacent to the angle x to the hypotenuse in a right triangle. The cosine function is periodic with a period of 2π, which means it repeats itself every 2π units.

Now, let’s consider the expression cos(-x). Here, the negative sign is applied to the angle x.

To understand cos(-x), we can use the identity cos(-x) = cos(x). This identity states that the cosine function of a negative angle is equal to the cosine function of the positive angle.

This is because the cosine function is an even function, which means it is symmetrical about the y-axis. The values of cos(x) and cos(-x) are the same for any given angle x.

Therefore, cos(-x) is equal to cos(x). In other words, the cosine function of a negative angle is equal to the cosine of the corresponding positive angle.

More Answers:

Formula for cos^2x in terms of Double Angle
Determining sin^2(2x) using the double angle identity for sine
Understanding the Concept of sin(-x): Evaluating the Sine of Negative Angles and Its Relationship with the Positive Counterpart

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