Explaining the Tangent Function and Its Behavior for Negative Angles in Mathematics

tan(-x)

In mathematics, the tangent function (tan) is a trigonometric function that relates the ratio of the lengths of the opposite and adjacent sides of a right triangle

In mathematics, the tangent function (tan) is a trigonometric function that relates the ratio of the lengths of the opposite and adjacent sides of a right triangle. It is defined as the ratio of the sine of an angle to the cosine of the same angle.

In the case of tan(-x), the negative sign is applied to the angle x. The tangent function for negative angles follows the same rules as for positive angles.

To determine the value of tan(-x), you can use the properties of the tangent function. One of the main properties is that tan(-x) is equal to -tan(x). This means that the tangent of a negative angle is equal to the negative of the tangent of the corresponding positive angle.

So, if you know the value of tan(x), you can find tan(-x) by taking the negative of that value. Conversely, if you know the value of tan(-x) and want to find tan(x), you can take the negative of tan(-x).

For example, if tan(x) = 0.5, then tan(-x) = -0.5. Similarly, if tan(-x) = -1.2, then tan(x) = 1.2.

It’s important to note that the tangent function has certain limitations. It is not defined for angles that are multiple of pi/2 radians (90 degrees) plus k*pi radians, where k is an integer. At these angles, the tangent function approaches infinity (or negative infinity) and is said to be undefined.

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