To isolate \( x \) from the equation \( y = \tan(x) \), you need to apply the inverse tangent function (also known as arctangent) to both sides. Here's the step-by-step process:

1. Start with the given equation:
   \[
   y = \tan(x)
   \]

2. Apply the inverse tangent function to both sides:
   \[
   x = \arctan(y)
   \]

So, the isolated form of \( x \) is:
\[
x = \arctan(y)
\]

Would you like more details on the inverse trigonometric functions, or do you have any other questions?

Here are some related questions you might find interesting:

1. How do you differentiate the function \( y = \tan(x) \)?
2. What is the range of the function \( x = \arctan(y) \)?
3. How do you solve \( \tan(x) = 1 \) for \( x \)?
4. What is the general solution for \( x = \arctan(y) \) in trigonometry?
5. How does the graph of \( y = \arctan(x) \) look like?

**Tip:** Remember that \( \arctan(y) \) gives you an angle whose tangent is \( y \), and its principal value is usually in the range \( -\frac{\pi}{2} \) to \( \frac{\pi}{2} \).

Learn how to isolate x from the equation y = tan(x) using the inverse tangent function (arctangent). This problem covers trigonometric concepts and the application of inverse trigonometric functions. Suitable for advanced high school students (Grades 11-12).

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