Inverse Cosecant Function for Numeric and Symbolic Arguments

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

Compute the inverse cosecant function for these numbers. Because these numbers are not symbolic objects,acscreturns 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,acscreturns 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)]

Usevpato approximate symbolic results with floating-point numbers:

vpa(symA)

ans = [ -0.52359877559829887307710723054658,... Inf,... 1.0471975511965977461542144610932,... 1.5707963267948966192313216916398... - 1.3169578969248165734029498707969i,... 1.5707963267948966192313216916398,... 0.20135792079033079660099758712022]

Plot Inverse Cosecant Function

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

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

Handle Expressions Containing Inverse Cosecant Function

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

找到反整合函数的第一个和第二个衍生物：

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