What is arctan 1?

Understand the Problem

The question is asking for the value of the inverse tangent (arctan) of 1, which is a key concept in trigonometry. The arctan function takes a value and returns the angle whose tangent is that value.

Answer

\( \frac{\pi}{4} \)
Answer for screen readers

The final answer is ( \frac{\pi}{4} )

Steps to Solve

  1. Understand what arctan represents

    The arctan function, also known as inverse tangent, returns the angle whose tangent is the given number.

  2. Set up the equation

    To find $\arctan(1)$, set up the equation $\theta = \arctan(1)$ which means $\tan(\theta) = 1$.

  3. Find the angle whose tangent is 1

    Determine the angle $\theta$ such that $\tan(\theta) = 1$. The angle in the unit circle that satisfies this equation is $\frac{\pi}{4}$ radians (which is 45 degrees).

    $$ \tan \left( \frac{\pi}{4} \right) = 1 $$

  4. Conclude the answer

    Therefore, $\arctan(1) = \frac{\pi}{4}$ radians.

The final answer is ( \frac{\pi}{4} )

More Information

The angle ( \frac{\pi}{4} ) radians is equivalent to 45 degrees, which is a standard angle in trigonometry.

Tips

A common mistake is to forget that arctan returns the angle whose tangent is the given value. Always refer to the unit circle for standard values.

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