Inverse Tangent Function for Numeric and Symbolic Arguments

Depending on its arguments,atanreturns floating-point or exact symbolic results.

Compute the inverse tangent function for these numbers. Because these numbers are not symbolic objects,atanreturns floating-point results.

A = atan([-1, -1/3, -1/sqrt(3), 1/2, 1, sqrt(3)])

A = -0.7854 -0.3218 -0.5236 0.4636 0.7854 1.0472

Compute the inverse tangent function for the numbers converted to symbolic objects. For many symbolic (exact) numbers,atanreturns unresolved symbolic calls.

symA = atan(sym([-1, -1/3, -1/sqrt(3), 1/2, 1, sqrt(3)]))

symA = [ -pi/4, -atan(1/3), -pi/6, atan(1/2), pi/4, pi/3]

Usevpato approximate symbolic results with floating-point numbers:

vpa(symA)

ans = [ -0.78539816339744830961566084581988,... -0.32175055439664219340140461435866,... -0.52359877559829887307710723054658,... 0.46364760900080611621425623146121,... 0.78539816339744830961566084581988,... 1.0471975511965977461542144610932]

Plot Inverse Tangent Function

Plot the inverse tangent function on the interval from -10 to 10.

symsxfplot(atan(x),[-10 10]) gridon

Handle Expressions Containing Inverse Tangent Function

Many functions, such asdiff,int,taylor, andrewrite, can handle expressions containingatan.

Find the first and second derivatives of the inverse tangent function:

syms x diff(atan(x), x) diff(atan(x), x, x)

ans = 1/(x^2 + 1) ans = -(2*x)/(x^2 + 1)^2

Find the indefinite integral of the inverse tangent function:

int(atan(x), x)

ans = x*atan(x) - log(x^2 + 1)/2

Find the Taylor series expansion ofatan(x):

taylor(atan(x), x)

ans = x^5/5 - x^3/3 + x

Rewrite the inverse tangent function in terms of the natural logarithm:

rewrite(atan(x), 'log')

ans = (log(1 - x*1i)*1i)/2 - (log(1 + x*1i)*1i)/2