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
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Understand what arctan represents
The arctan function, also known as inverse tangent, returns the angle whose tangent is the given number.
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Set up the equation
To find $\arctan(1)$, set up the equation $\theta = \arctan(1)$ which means $\tan(\theta) = 1$.
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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).
$$ \tan \left( \frac{\pi}{4} \right) = 1 $$
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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.
