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arccos(x) = cos-1(x)
Rule name | Rule |
---|---|
Cosine of arccosine | cos( arccos x ) = x |
Arccosine of cosine | arccos( cos x ) = x + 2kπ, when k∈ℤ (k is integer) |
Arccos of negative argument | arccos(-x) = π - arccos x = 180° - arccos x |
Complementary angles | arccos x = π/2 - arcsin x= 90° - arcsin x |
Arccos sum | arccos(α) + arccos(β) = arccos( αβ - √(1-α2)(1-β2) ) |
Arccos difference | arccos(α) - arccos(β) = arccos( αβ + √(1-α2)(1-β2) ) |
Arccos of sin of x | arccos( sin x ) = -x - (2k+0.5)π |
Sine of arccosine | ![]() |
Tangent of arccosine | ![]() |
Derivative of arccosine | ![]() |
Indefinite integral of arccosine | ![]() |
x | arccos(x) | |
---|---|---|
degrees | radians | |
-1 | 180° | π |
-0.8660254 | 150° | 5π/6 |
-0.7071068 | 135° | 3π/4 |
-0.5 | 120° | 2π/3 |
0 | 90° | π/2 |
0.5 | 60° | π/3 |
0.7071068 | 45° | π/4 |
0.8660254 | 30° | π/6 |
1 | 0° | 0 |