Arctan (x), tan -1 (x), feidhm tadhlaí inbhéartaigh .
Sainmhínítear arctangent x mar fheidhm tadhlaí inbhéartaigh x nuair atá x fíor (x ∈ℝ ).
Nuair atá tadhlaí y cothrom le x:
tan y = x
Ansin tá an t-arctangent de x cothrom le feidhm tadhlaí inbhéartaigh x, atá cothrom le y:
arctan x = tan -1 x = y
arctan 1 = tan -1 1 = π / 4 rad = 45 °
Ainm na rialach | Riail |
---|---|
Tadhlaí arctangent |
tan (arctan x ) = x |
Arctan argóint dhiúltach |
arctan (- x ) = - arctan x |
Suim Arctan |
arctan α + arctan β = arctan [( α + β ) / (1- αβ )] |
Difríocht Arctan |
arctan α - arctan β = arctan [( α - β ) / (1+ αβ )] |
Sín arctangent |
|
Cosine arctangent |
|
Argóint chómhalartach |
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Arctan ó arcsin |
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Díorthach arctan |
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Cuid dhílis éiginnte den arctan |
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x | arctan (x) (rad) |
arctan (x) (°) |
---|---|---|
-∞ | -π / 2 | -90 ° |
-3 | -1.2490 | -71.565 ° |
-2 | -1.1071 | -63.435 ° |
-√ 3 | -π / 3 | -60 ° |
-1 | -π / 4 | -45 ° |
-1 / √ 3 | -π / 6 | -30 ° |
-0.5 | -0.4636 | -26.565 ° |
0 | 0 | 0 ° |
0.5 | 0.4636 | 26.565 ° |
1 / √ 3 | π / 6 | 30 ° |
1 | π / 4 | 45 ° |
√ 3 | π / 3 | 60 ° |
2 | 1.1071 | 63.435 ° |
3 | 1.2490 | 71.565 ° |
∞ | π / 2 | 90 ° |
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