象征性的逆余割ant function
acsc(
returns the inverse cosecant function (arccosecant function) ofX
)X
. All angles are in radians.
For real values ofX
in intervals[-Inf,-1]
and[1,Inf]
,acsc
returns real values in the interval[-pi/2,pi/2]
.
For real values ofX
in the interval[1]
and for complex values ofX
,acsc
returns complex values with the real parts in the interval[-pi/2,pi/2]
.
Depending on its arguments,acsc
returns floating-point or exact symbolic results.
Compute the inverse cosecant function for these numbers. Because these numbers are not symbolic objects,acsc
returns floating-point results.
A = acsc([-2, 0, 2/sqrt(3), 1/2, 1, 5])
A = -0.5236 + 0.0000i 1.5708 - Infi 1.0472 + 0.0000i 1.5708... - 1.3170i 1.5708 + 0.0000i 0.2014 + 0.0000i
Compute the inverse cosecant function for the numbers converted to symbolic objects. For many symbolic (exact) numbers,acsc
returns unresolved symbolic calls.
symA = acsc(sym([-2, 0, 2/sqrt(3), 1/2, 1, 5]))
symA = [ -pi/6, Inf, pi/3, asin(2), pi/2, asin(1/5)]
Usevpa
to approximate symbolic results with floating-point numbers:
vpa(symA)
ans = [ -0.52359877559829887307710723054658,... Inf,... 1.0471975511965977461542144610932,... 1.5707963267948966192313216916398... - 1.3169578969248165734029498707969i,... 1.5707963267948966192313216916398,... 0.20135792079033079660099758712022]
Plot the inverse cosecant function on the interval from -10 to 10.
symsxfplot(acsc(x),[-10 10]) gridon
Many functions, such asdiff
,int
,taylor
, andrewrite
, can handle expressions containingacsc
.
Find the first and second derivatives of the inverse cosecant function:
syms x diff(acsc(x), x) diff(acsc(x), x, x)
ans = -1/(x^2*(1 - 1/x^2)^(1/2)) ans = 2/(x^3*(1 - 1/x^2)^(1/2)) + 1/(x^5*(1 - 1/x^2)^(3/2))
Find the indefinite integral of the inverse cosecant function:
int(acsc(x), x)
ans = x*asin(1/x) + log(x + (x^2 - 1)^(1/2))*sign(x)
Find the Taylor series expansion ofacsc(x)
aroundx = Inf
:
taylor(acsc(x), x, Inf)
ans = 1 / x + 1 / (6 * x ^ 3) + 3 / (40 * x ^ 5)
Rewrite the inverse cosecant function in terms of the natural logarithm:
rewrite(acsc(x), 'log')
ans = -log(1i/x + (1 - 1/x^2)^(1/2))*1i