In mathematics, the inverse trigonometric functions are the inverse functions of the trigonometric functions.
arccos 0.5 = cos^1 0.5 = 60o 0' 0" = 60o + k×360o (k=..-1,0,1,..) = -300o, 60o, 420o, .. = 1.04719755rad + k×2π (k=..-1,0,1,..) = -1.66666667π, 0.33333333π, 2.33333333π, ..
arccos -0.3 = cos^1 -0.3 = 107o 27' 27.371" = 107.45760312o + k×360o (k=..-1,0,1,..) = -252.54239688o, 107.45760312o, 467.45760312o, .. = 1.87548898rad + k×2π (k=..-1,0,1,..) = -1.40301332π, 0.59698668π, 2.59698668π, ..
y=arccos(x) Graph |
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Name | Usual notation | Definition | Domain of x for real result | Range of usual principal value (radians) |
Range of usual principal value (degrees) |
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arcsine | y = arcsin x | x = sin y | -1 ≤ x ≤ 1 | -π/2 ≤ y ≤ π/2 | -90° ≤ y ≤ 90° |
arccosine | y = arccos x | x = cos y | -1 ≤ x ≤ 1 | 0 ≤ y ≤ π | 0° ≤ y ≤ 180° |
arctangent | y = arctan x | x = tan y | all real numbers | -π/2 < y < π/2 | -90° < y < 90° |
arccotangent | y = arccot x | x = cot y | all real numbers | 0 < y < π | 0° < y < 180° |
arcsecant | y = arcsec x | x = sec y | x ≤ -1 or 1 ≤ x | 0 ≤ y < π/2 or π/2 < y ≤ π | 0° ≤ y < 90° or 90° < y ≤ 180° |
arccosecant | y = arccsc x | x = csc y | x ≤ -1 or 1 ≤ x | -π/2 ≤ y < 0 or 0 < y ≤ π/2 | -90° ≤ y < 0° or 0° < y ≤ 90° |