Quite simple, perl (and most other programming languages)
take angles for trig functions in radians, while calculators
take them in degrees, radians or gradians (usually). Most people
prefer degrees, but radians are nicer to mathamaticians and
other similar people.
The best thing for you to do is
$num = sin( deg2rad( 45 ) );
I think Math::Trig
is part of the standard perl distribution, so read the documentation and go for it.
Update: I know about the math of radians as jepri explained but after the amount of it i've done at school recently I didn't feel like providing an explanation.