arccosine การใช้

• This formula involves only real terms if and the argument of the arccosine is between and.
• Intuitively I expect a function full of cosines to be inverted by a function full of arccosines.
• The function available are Sine, Arcsine, Cosine, Arccosine, Tangent, Arctangent, Logarithm and Antilogarithm.
• If is complex or is greater than 2 in absolute value, the arccosine should be taken along the same branch for all three values of.
• Nevertheless, purely real expressions of the solutions may be obtained using hypergeometric functions, or more elementarily in terms of trigonometric functions, specifically in terms of the cosine and arccosine functions.
• For angles near 0 and, arccosine is ill-conditioned and will thus calculate the angle with reduced accuracy in a computer implementation ( due to the limited number of digits ).
• In the math world, can arcsine, arccosine, arctangent, etc . or sin-1, cos-1, tan-1, etc . be officially called inverse trigonometric functions?
• Often, the hypotenuse is unknown and would need to be calculated before using arcsine or arccosine using the Pythagorean Theorem : a ^ 2 + b ^ 2 = h ^ 2 where h is the length of the hypotenuse.
• As one can see from the form involving arccosine, the derivative of the time of flight with respect to " d " ( or ? ) goes to zero as " d " approaches 20 000 km ( halfway around the world ).
• Can one prove that there's "'no bijection "'- from the set of ( continuous ) Arccosine functions-to the set of ( continuous ) Arctan functions, so that the bijection is induced by a first-order formula which:
• The formulas which follow, due to Fran鏾is Vi鑤e, are true in general ( except when " p " = 0 ), and are purely real when the equation has three real roots, but involve complex cosines and arccosines when there is only one real root.
• :* Contains no free variables, and contains logical symbols only ( including identity ), except for one function-symbol "'interpreted ( in advance ) as an Arccosine "'function, and another function symbol "'interpreted ( in advance ) as an Arctan "'function?
• Near multiples of 180? care is needed to avoid numerical problems : in extracting the angle, a two-argument arctangent with atan2 ( sin ?, cos ? ) equal to ? avoids the insensitivity of arccosine; and in computing the axis magnitude in order to force unit magnitude, a brute-force approach can lose accuracy through underflow.
• :For the arccosine to be defined, its argument must be between  " 1 and + 1, and this fails when the radius goes below the stated limit . ( A similar problem occurs with the formula for " A ", where a quantity inside a square root goes negative . ) Both algebra and geometry are telling us we cannot step carelessly into the domain of small radii.