when called with an _Imaginary (not _Complex) argument, the following apply:

cos(iy) = cosh(y)
sin(iy) = i sinh(y)
tan(iy) = i tanh(y)
cosh(iy) = cos(y)
sinh(iy) = i sin(y)
tanh(iy) = i tan(y)
asin(iy) = i asinh(y)
atan(iy) = i atanh(y)
asinh(iy) = i asin(y)
atanh(iy) = i atan(y)

cos, cosh, fabs, carg, cimag, and creal => return real types
sin, tan, sinh, tanh, asin, atan, asinh, atanh => return _Imaginary types
all others => return _Complex types