Symbolic inverse tangent function
Depending on its arguments, atan
returns
floating-point or exact symbolic results.
Compute the inverse tangent function for these numbers. Because
these numbers are not symbolic objects, atan
returns
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, atan
returns
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]
Use vpa
to approximate symbolic results
with floating-point numbers:
vpa(symA)
ans = [ -0.78539816339744830961566084581988,... -0.32175055439664219340140461435866,... -0.52359877559829887307710723054658,... 0.46364760900080611621425623146121,... 0.78539816339744830961566084581988,... 1.0471975511965977461542144610932]
Plot the inverse tangent function on the interval from -10 to 10.
syms x fplot(atan(x),[-10 10]) grid on
Many functions, such as diff
, int
, taylor
,
and rewrite
, can handle expressions containing atan
.
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 of atan(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