Fill in the blank:
Gamma = 2(inverse tangent of e to the x) minus pi/2 is the _________ of x.
The expression Gamma = 2(arctan(e^x)) - π/2 is the angle of x.
To fill in the blank, we need to determine what mathematical term represents the result of the expression mentioned. Let's break down the given equation and explain each step:
1. Gamma = 2 * invtan(e^x) - π/2
The equation involves the inverse tangent function (arctan or atan), exponential function (e^x), and Pi (π).
2. The inverse tangent function (atan) finds the angle whose tangent is a given value. Here, we're using it to find the angle whose tangent is e^x.
3. Multiply the result of the inverse tangent by 2.
4. Subtract π/2 from the previous result.
Now, to find the missing term, we need to identify what the equation represents. In mathematics, an equation that gives the value of a variable (here, x) in terms of another variable(s) is known as an "equation of representation."
Therefore, the missing term would be the "equation of representation" or "representation" of x.