Solve for y: arctan(y) = x^2 + c

Understand the Problem

The question asks to solve the equation $\arctan(y) = x^2 + c$ for $y$. We can solve this by taking the tangent of both sides of the equation to isolate $y$.

Answer

$y = \tan(x^2 + c)$

Steps to Solve

Take the tangent of both sides

To isolate $y$, take the tangent of both sides of the equation:

$$ \tan(\arctan(y)) = \tan(x^2 + c) $$

Simplify the left side

Since $\tan$ and $\arctan$ are inverse functions, they cancel out on the left side:

$$ y = \tan(x^2 + c) $$

$y = \tan(x^2 + c)$

More Information

The tangent function has a period of $\pi$, so the function repeats every $\pi$ units.

Tips

A common mistake is not remembering to take the tangent of the entire right side, including the constant $c$.

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