Fill in the blank:
gamma = 2(inverse tangent of e to the x) - pi/2 is the _______ of x.
To fill in the blank, we need to determine the name of the mathematical function that represents the expression gamma = 2(inverse tangent of e to the x) - pi/2.
Let's break down the expression step by step:
1. Start with e to the x: This represents the exponential function, where e is Euler's number (approximately 2.718) and x is the exponent.
2. Take the inverse tangent of e to the x: This means finding the angle whose tangent is equal to e to the x. The inverse tangent function is usually denoted as arctan or atan.
3. Multiply the result by 2: This doubles the value obtained from step 2.
4. Subtract pi/2 from the previous result: This subtracts the value of pi/2 (approximately 1.571) from the doubled inverse tangent.
Now that we understand the expression, let's find the name of the function that represents it. The function is γ (gamma), which is equal to the given expression.
Therefore, the blank can be filled with "gamma."