In most general math library implementations (e.g., the library in glibc, musl, etc.), the implementation of sin, as with most functions, is going to be a polynomial evaluation. See, e.g., https://github.com/kraj/musl/blob/kraj/master/src/math/__cos... for the implementation in musl, or https://github.com/bminor/glibc/blob/master/sysdeps/ieee754/... for glibc's implementation.
Of course, if you're not using a standard math library implementation, you're probably preferring speed over accuracy, and so you might use a lookup table and linear interpolation to get a very coarse approximation instead.
Tend to use radians because we're moving from written proofs or simulations into embedded code in such systems. The code needs to read and work the same as those.
edit: Sorry, to clarify, this was a function involving trigonometry but not simply vanilla sine or cosine. However, angular values being represented in radians did help in the same way I described in the parent post.
So mathematical libraries in WASM reimplement the trigonometric functions using series.
Example: https://github.com/WebAssembly/wasi-libc/blob/2e6fb9d8ee0cdf...