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Definition df-acos 25376
Description: Define the arccosine function. See also remarks for df-asin 25375. Since we define arccos in terms of arcsin, it shares the same branch points and cuts, namely (-∞, -1) ∪ (1, +∞). (Contributed by Mario Carneiro, 31-Mar-2015.)
Assertion
Ref Expression
df-acos arccos = (𝑥 ∈ ℂ ↦ ((π / 2) − (arcsin‘𝑥)))

Detailed syntax breakdown of Definition df-acos
StepHypRef Expression
1 cacos 25373 . 2 class arccos
2 vx . . 3 setvar 𝑥
3 cc 10529 . . 3 class
4 cpi 15415 . . . . 5 class π
5 c2 11686 . . . . 5 class 2
6 cdiv 11291 . . . . 5 class /
74, 5, 6co 7150 . . . 4 class (π / 2)
82cv 1529 . . . . 5 class 𝑥
9 casin 25372 . . . . 5 class arcsin
108, 9cfv 6354 . . . 4 class (arcsin‘𝑥)
11 cmin 10864 . . . 4 class
127, 10, 11co 7150 . . 3 class ((π / 2) − (arcsin‘𝑥))
132, 3, 12cmpt 5143 . 2 class (𝑥 ∈ ℂ ↦ ((π / 2) − (arcsin‘𝑥)))
141, 13wceq 1530 1 wff arccos = (𝑥 ∈ ℂ ↦ ((π / 2) − (arcsin‘𝑥)))
Colors of variables: wff setvar class
This definition is referenced by:  acosf  25384  acosval  25393  dvacos  34865
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