tan (x), feidhm tadhlaí.
I dtriantán ceart ABC sainmhínítear tadhlaí α, tan (α) mar an cóimheas idir an taobh thall le huillinn α agus an taobh in aice leis an uillinn α:
tan α = a / b
a = 3 "
b = 4 "
tan α = a / b = 3/4 = 0.75
TBD
| Ainm na rialach | Riail |
|---|---|
| Siméadracht | tan (- θ ) = -tan θ |
| Siméadracht | tan (90 ° - θ ) = cot θ |
| tan θ = sin θ / cos θ | |
| tan θ = 1 / cot θ | |
| Uillinn dhúbailte | tan 2 θ = 2 tan θ / (1 - tan 2 θ ) |
| Suim uillinneacha | tan ( α + β ) = (tan α + tan β ) / (1 - tan α tan β ) |
| Difríocht uillinneacha | tan ( α - β ) = (tan α - tan β ) / (1 + tan α tan β ) |
| Díorthach | tan ' x = 1 / cos 2 ( x ) |
| Lárnach | ∫ tan x d x = - ln | cos x | + C. |
| Foirmle Euler | tan x = ( e ix - e - ix ) / i ( e ix + e - ix ) |
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 °
Féach: Feidhm Arctan
| x (rad) |
x (°) |
tan (x) |
|---|---|---|
| -π / 2 | -90 ° | -∞ |
| -1.2490 | -71.565 ° | -3 |
| -1.1071 | -63.435 ° | -2 |
| -π / 3 | -60 ° | -√ 3 |
| -π / 4 | -45 ° | -1 |
| -π / 6 | -30 ° | -1 / √ 3 |
| -0.4636 | -26.565 ° | -0.5 |
| 0 | 0 ° | 0 |
| 0.4636 | 26.565 ° | 0.5 |
| π / 6 | 30 ° | 1 / √ 3 |
| π / 4 | 45 ° | 1 |
| π / 3 | 60 ° | √ 3 |
| 1.1071 | 63.435 ° | 2 |
| 1.2490 | 71.565 ° | 3 |
| π / 2 | 90 ° | ∞ |
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