To determine the value of [tex]\(\tan(60^\circ)\)[/tex], it's important to remember the definition and properties of the tangent function. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. However, for angles commonly used in trigonometry, we can use their known values.
Let's consider the tangent values of commonly known angles in the unit circle:
- [tex]\(\tan(0^\circ) = 0\)[/tex]
- [tex]\(\tan(30^\circ) = \frac{1}{\sqrt{3}}\)[/tex]
- [tex]\(\tan(45^\circ) = 1\)[/tex]
- [tex]\(\tan(60^\circ) = \sqrt{3}\)[/tex]
- [tex]\(\tan(90^\circ)\)[/tex] is undefined
Given that we need to find [tex]\(\tan(60^\circ)\)[/tex], the tangent of [tex]\(60^\circ\)[/tex] is known to be [tex]\(\sqrt{3}\)[/tex].
Hence, the value of [tex]\(\tan(60^\circ)\)[/tex] is:
[tex]\[
\boxed{\sqrt{3}}
\][/tex]
