arcsine is what you call for sine cosine and tangent.
what do you call sine cosine and tangent?
arcsine
tangent half-angle formula





























in trigonometry, tangent half-angle formulas relate the tangent of half of an angle to trigonometric functions of the entire angle. among these are the following





























from these one can derive identities expressing the sine, cosine, and tangent as functions of tangents of half-angles:





























section::::proofs.





























section::::proofs.:algebraic proofs.





























use double-angle formulae and ,





























taking the quotient of the formulae for sine and cosine yields





























combining the pythagorean identity formula_6 with the double-angle formula for the cosine, formula_7, 





























rearranging, and taking the square roots yields 





























formula_8 and formula_9





























which, upon division gives
tangent half-angle formula
bullet::::- the cosine of angle "a" is the hyperbolic tangent of the adjacent leg divided by the hyperbolic tangent of the hypotenuse.





























bullet::::- the tangent of angle "a" is the hyperbolic tangent of the opposite leg divided by the hyperbolic sine of the adjacent leg.





























bullet::::- the hyperbolic cosine of the adjacent leg to angle a is the cosine of angle b divided by the sine of angle a.





























bullet::::- the hyperbolic cosine of the hypotenuse is the product of the hyperbolic cosines of the legs.
hyperbolic triangle