Osbourne's Rule

I came about an interesting rule the other day for converting a trigometric function into a hyperbolic.

You can take some trigometric functions such as:

i ) sin(A+B) = sinA.cosB + cosA.sinB
ii) cos(A+B) = cosA.cosB - sinA.sinB

from here, if there is a sin.sin then the sign changes. Otherwise its exactly the same.

So the above become:

i) sinh(A+B) = sinhA.coshB + coshA.sinhB
ii) cosh(A+B) = sinhA.coshB + sinhA.sinhB

This might be a simple math rule to most, but in the past I had always found the functions by substituting their exponential equivalents in, and re-arrganging.

This makes things alot simpler