tan-5n over 3

To simplify the expression tan(-5n)/3, we need to understand the trigonometric function tangent (tan) and apply the rules of trigonometry.

The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle.

To simplify tan(-5n)/3, we need to consider the properties of the tangent function. The tangent function is periodic with a period of π (pi). This means that tan(x) = tan(x + nπ), where n is an integer.

Since the expression is tan(-5n)/3, we can rewrite it as tan(-5n + 0π)/3. Now, applying the periodicity property, we can rewrite it as tan((-5n + 6π)/3)/3.

To further simplify the expression, we need to find the common factors between the numerator and the denominator. In this case, since the denominator is 3, there are no common factors.

Therefore, the simplified expression is tan((-5n + 6π)/3)/3.