Final answer:
The arctangent of 1/√3 correctly returns π/3, as the standard range for arctangent doesn't present an issue in this case. Therefore, the correct answer is c) Doesn't return a value within the standard range of arctangent.
Step-by-step explanation:
The problem with finding the arctangent of 1/√3 relates to identifying the correct angle that corresponds to this value. In trigonometry, the arctangent function is used to find the angle whose tangent value is the number provided as the argument to the function.
The correct answer to the question is b) Returns π/3 because tan(π/6) = √3/3 and not 1/√3. Therefore, the arctangent or inverse tangent of 1/√3, which simplifies to √3/3, actually returns π/3. This aligns with the standard range for arctangent, meaning there is no issue with the value being out of range.
The problem with finding the arctangent of 1/root3 is that it does not return a value within the standard range of arctangent.
The arctangent function returns angles between -π/2 and π/2, or -90° and 90°. In this case, the value 1/root3 is approximately 0.577, which is less than 1. So, the arctangent of 1/root3 is an angle smaller than 45°.
Therefore, the correct answer is c) Doesn't return a value within the standard range of arctangent.