sincos – Most modern CPUs have a built-in instruction called sincos(x) that returns both the sine and the cosine of x. In scientific computations, often you need both in your computation. So instead of calling sin and cos separately, see if your programming language supports the sincos function, which is often just a thin wrapper to the processor intrinsic function. If it does, you can get a 2x speedup in your trig calls for free.

exp2 – If you are raising 2 to a power, exp2(x) is much faster than pow(2,x).

expm1, log1p – For arguments close to 1, exp(x)-1 and log(1+x) suffer from significant loss of precision. To avoid this, you can use expm1(x) and log1p(x), respectively, instead, both of which compute the same thing using a different approximation with better error properties for values of x close to 1.

atan2 – If you are taking the arctangent of a ratio, atan(y/x), then you cannot distinguish between y/x and -y/(-x) or -y/x and y/(-x). If you need to separate out all four quadrants, then you can use atan2(y, x) which gives you the correct sign of the angle considering all four quadrants.