aaaa202 said:
The value of arctan(1) is equal to π/4 or approximately 0.7854 radians. This can also be written as 45 degrees in terms of degrees.
To evaluate arctan(0), we can use the definition of arctan as the inverse of tangent. Since tangent is equal to opposite over adjacent in a right triangle, we can create a right triangle with one side as 0 and the other side as any non-zero value. The angle opposite the side with value 0 will be the value of arctan(0).
The range of arctan is restricted to the interval of -π/2 to π/2 because this is the range of values for which the tangent function is one-to-one. In other words, for every x-value in this range, there is only one corresponding y-value for tangent and thus, for arctan as well.
Arctan is the inverse of tangent, meaning that it is the angle whose tangent is a given value. It is also related to the other trigonometric functions through the identities tan(x) = sin(x)/cos(x) and arctan(x) = arccos(1/x) = arcsin(x/√(1+x^2)).
The main difference between arctan(1) and arctan(0) is their values. As mentioned before, arctan(1) is equal to π/4 or 45 degrees, while arctan(0) is equal to 0. Additionally, arctan(1) represents the angle whose tangent is 1, while arctan(0) represents the angle whose tangent is 0.