What is the value of arctan(0)?
Understand the Problem
The question is asking for the value of the arctangent function when the input is 0. The arctangent function returns the angle whose tangent is the given number.
Answer
0 radians or 0°
Answer for screen readers
The final answer is 0 radians or 0°
Steps to Solve
- Recall the definition of arctangent
The arctangent function, $ an^{-1}(x)$, returns the angle whose tangent is $x$.
- Identify the angle whose tangent is 0
We need to find the angle $ heta$ such that $ an( heta) = 0$. Tangent is the ratio of the opposite side to the adjacent side in a right triangle. When $ heta=0$, there is no opposite side, so $ an(0^ ext{°}) = 0$.
- Write the final answer
Thus, $ an^{-1}(0) = 0^ ext{°}$.
The final answer is 0 radians or 0°
More Information
The arctangent of 0 can be represented in both radians and degrees. In this case, it's 0 radians or 0°.
Tips
A common mistake is to confuse the input and the output of the arctangent function. Ensure you're finding the angle whose tangent is the given value.
