- #1
cragar
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my math teacher said that the arctan can be setup in terms of logs
does anyone know how to do this.
does anyone know how to do this.
Arctan(x) in terms of logs is defined as the inverse function of the tangent function when expressed in terms of logarithms. It represents the angle whose tangent is equal to x, where x is a real number.
To express arctan(x) in terms of natural logs, you can use the identity arctan(x) = ln((1+x)/(1-x))/2. This means that the natural log of the fraction (1+x)/(1-x) divided by 2 is equal to the arctan of x.
Yes, arctan(x) can be written as a combination of other trigonometric functions. It is equal to 1/2 * ln((1+x)/(1-x)), which can be expressed in terms of the sine and cosine functions using the identities sin(x) = (1/2i)(e^ix - e^-ix) and cos(x) = (1/2)(e^ix + e^-ix).
To evaluate arctan(x) in terms of logs, you can use a calculator or a table of logarithms. You can also use the Taylor series expansion for arctan(x): arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... This allows you to approximate the value of arctan(x) by using the logarithms of the terms in the series.
The domain of arctan(x) in terms of logs is all real numbers except -1 and 1. The range is from -pi/2 to pi/2, or from -90 to 90 degrees. This is because the tangent function is undefined at -pi/2 and pi/2, and as the inverse of the tangent function, arctan(x) also cannot be defined at these values.