Understanding the Tangent Function and its Behavior with Negative Angles

tan(-x)

The tangent function (tan) is a trigonometric function that relates the ratio of the opposite side to the adjacent side of a right triangle

The tangent function (tan) is a trigonometric function that relates the ratio of the opposite side to the adjacent side of a right triangle. However, the tangent function can also be defined for any angle (not just right angles) using the unit circle.

The tangent function is defined as:

tan(x) = sin(x) / cos(x),

where sin(x) is the sine function and cos(x) is the cosine function.

Now, let’s consider tan(-x). When we have a negative angle, it means the angle is measured clockwise instead of counterclockwise.

Since the tangent function is defined as the ratio of sin(x) / cos(x), let’s look at what happens when we substitute -x into the tangent function:

tan(-x) = sin(-x) / cos(-x).

The sine function is an odd function, meaning that sin(-x) = -sin(x). So, we can rewrite the expression as:

tan(-x) = -sin(x) / cos(-x).

The cosine function is an even function, meaning that cos(-x) = cos(x). Substituting this into the expression, we get:

tan(-x) = -sin(x) / cos(x).

So, to summarize, the tangent of a negative angle is equal to the negative tangent of the positive angle. This means that the sign of the tangent function will be flipped when dealing with negative angles.

More Answers: