Inverse Cosecant Function for Numeric and Symbolic Arguments

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)]

Use vpa 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 Inverse Cosecant Function

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

syms x
fplot(acsc(x),[-10 10])
grid on

Handle Expressions Containing Inverse Cosecant Function

Many functions, such as diff, int, taylor, and rewrite, can handle expressions containing acsc.

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 of acsc(x) around x = 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