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Mirrors > Home > MPE Home > Th. List > df-acos | Structured version Visualization version Unicode version |
Description: Define the arccosine function. See also remarks for df-asin 24592. Since we define arccos in terms of arcsin, it shares the same branch points and cuts, namely . (Contributed by Mario Carneiro, 31-Mar-2015.) |
Ref | Expression |
---|---|
df-acos | arccos arcsin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cacos 24590 | . 2 arccos | |
2 | vx | . . 3 | |
3 | cc 9934 | . . 3 | |
4 | cpi 14797 | . . . . 5 | |
5 | c2 11070 | . . . . 5 | |
6 | cdiv 10684 | . . . . 5 | |
7 | 4, 5, 6 | co 6650 | . . . 4 |
8 | 2 | cv 1482 | . . . . 5 |
9 | casin 24589 | . . . . 5 arcsin | |
10 | 8, 9 | cfv 5888 | . . . 4 arcsin |
11 | cmin 10266 | . . . 4 | |
12 | 7, 10, 11 | co 6650 | . . 3 arcsin |
13 | 2, 3, 12 | cmpt 4729 | . 2 arcsin |
14 | 1, 13 | wceq 1483 | 1 arccos arcsin |
Colors of variables: wff setvar class |
This definition is referenced by: acosf 24601 acosval 24610 dvacos 33497 |
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