I'm very new to Perl but it seems to me you've got it right anyway.
Perl has a number of intrinsic functions available for performing mathematical calculations.

abs() # return the absolute value
atan2(y/x) # return the arctangent of y/x
cos() # return the cosine
hex() # return decimal value of a hexidecimal string
oct() # return decimal value of an octal string
sin() # return the sine
sqrt() # return the square root

so you would require...
$angle = sin($angle)