Trigonometria e Produto Escalar

 

󰁔󰁥󰁭󰁡󰀺 󰁐󰁲󰁯󰁤󰁵󰁴󰁯 󰁥󰁳󰁣󰁡󰁬󰁡󰁲 󰁥 󰁦󰁵󰁮󰃧󰃵󰁥󰁳 󰁴󰁲󰁩󰁧󰁯󰁮󰁯󰁭󰃩󰁴󰁲󰁩󰁣󰁡󰁳 (󰁒󰁥󰁶󰁩󰁳󰃵󰁥󰁳)

Nome_______________________ Data __/12/2013

P󰁲󰁯󰁰󰁯󰁳󰁴󰁡 󰁤󰁥 󰁴󰁲󰁡󰁢󰁡󰁬󰁨󰁯 󰁮󰂺10

󰀱󰀮  󰁕󰁭󰁡 󰁲󰁯󰁤󰁡 󰁧󰁩󰁧󰁡󰁮󰁴󰁥 󰁤󰁥 󰁵󰁭 󰁰󰁡󰁲󰁱󰁵󰁥 󰁤󰁥 󰁤󰁩󰁶󰁥󰁲󰁳󰃵󰁥󰁳 󰁴󰁥󰁭 󰁤󰁯󰁺󰁥 󰁣󰁡󰁤󰁥󰁩󰁲󰁡󰁳, 󰁮󰁵󰁭󰁥󰁲󰁡󰁤󰁡󰁳 󰁤󰁥 1 󰁡 12, 󰁣󰁯󰁭 󰁵󰁭 󰁬󰁵󰁧󰁡󰁲

󰁣󰁡󰁤󰁡 󰁵󰁭󰁡 (󰁶󰁥󰁲 󰁦󰁩󰁧󰁵󰁲󰁡 󰁡󰁢󰁡󰁩󰁸󰁯). S󰁥󰁩󰁳 󰁲󰁡󰁰󰁡󰁲󰁩󰁧󰁡󰁳 󰁥 󰁳󰁥󰁩󰁳 󰁲󰁡󰁰󰁡󰁺󰁥󰁳 󰁶󰃣󰁯 󰁡󰁮󰁤󰁡󰁲 󰁮󰁡 󰁲󰁯󰁤󰁡 󰁧󰁩󰁧󰁡󰁮󰁴󰁥. D󰁥󰁰󰁯󰁩󰁳 󰁤󰁥 󰁴󰁯󰁤󰁡 󰁡 󰁧󰁥󰁮󰁴󰁥 󰁥󰁳󰁴󰁡󰁲 󰁳󰁥󰁮󰁴󰁡󰁤󰁡 󰁮󰁡󰁳 󰁲󰁥󰁳󰁰󰁥󰁴󰁩󰁶󰁡󰁳 󰁣󰁡󰁤󰁥󰁩󰁲󰁡󰁳, 󰁡 󰁲󰁯󰁤󰁡 󰁧󰁩󰁧󰁡󰁮󰁴󰁥 󰁣󰁯󰁭󰁥󰃧󰁡 󰁡 󰁧󰁩󰁲󰁡󰁲. 󰁕󰁭 󰁤󰁯󰁳 󰁲󰁡󰁰󰁡󰁺󰁥󰁳, 󰁯 M󰁡󰁮󰁵󰁥󰁬, 󰁦󰁩󰁣󰁯󰁵 󰁳󰁥󰁮󰁴󰁡󰁤󰁯 󰁮󰁡 󰁣󰁡󰁤󰁥󰁩󰁲󰁡 󰁮󰃺󰁭󰁥󰁲󰁯 1. N󰁯 󰁩󰁮󰁳󰁴󰁡󰁮󰁴󰁥 󰁥󰁭 󰁱󰁵󰁥 󰁡 󰁲󰁯󰁤󰁡 󰁧󰁩󰁧󰁡󰁮󰁴󰁥 󰁣󰁯󰁭󰁥󰃧󰁡 󰁡 󰁧󰁩󰁲󰁡󰁲, 󰁡 󰁣󰁡󰁤󰁥󰁩󰁲󰁡 1 󰁥󰁳󰁴󰃡 󰁮󰁡 󰁰󰁯󰁳󰁩󰃧󰃣󰁯 󰁩󰁮󰁤󰁩󰁣󰁡󰁤󰁡 󰁮󰁡 󰁦󰁩󰁧󰁵󰁲󰁡 󰁡󰁣󰁩󰁭󰁡. A󰁤󰁭󰁩󰁴󰁡 󰁱󰁵󰁥 󰁡 󰁤󰁩󰁳󰁴󰃢󰁮󰁣󰁩󰁡, 󰁥󰁭 󰁭󰁥󰁴󰁲󰁯󰁳, 󰁤󰁡 󰁣󰁡󰁤󰁥󰁩󰁲󰁡 1 󰁡󰁯 󰁳󰁯󰁬󰁯, 󰁴 󰁳󰁥󰁧󰁵󰁮󰁤󰁯󰁳 󰁡󰁰󰃳󰁳 󰁡 󰁲󰁯󰁤󰁡 󰁧󰁩󰁧󰁡󰁮󰁴󰁥 󰁴󰁥󰁲 󰁣󰁯󰁭󰁥󰃧󰁡󰁤󰁯 󰁡 󰁧󰁩󰁲󰁡󰁲, 󰃩 󰁤󰁡󰁤󰁡 󰁰󰁯󰁲

d (t ) =

 

 π   t       30 

 

7 + 5sen

󰀱󰀮󰀱󰀮  D󰁥󰁴󰁥󰁲󰁭󰁩󰁮󰁡 󰁡 󰁤󰁩󰁳󰁴󰃢󰁮󰁣󰁩󰁡 󰁡 󰁱󰁵󰁥 󰁡 󰁣󰁡󰁤󰁥󰁩󰁲󰁡 󰁮󰃺󰁭󰁥󰁲󰁯 1 󰁳󰁥 󰁥󰁮󰁣󰁯󰁮󰁴󰁲󰁡 󰁤󰁯 󰁳󰁯󰁬󰁯 󰁮󰁯 󰁩󰁮󰁳󰁴󰁡󰁮󰁴󰁥 󰁩 󰁮󰁳󰁴󰁡󰁮󰁴󰁥 󰁥󰁭 󰁱󰁵󰁥 󰁡 󰁲󰁯󰁤󰁡

󰁧󰁩󰁧󰁡󰁮󰁴󰁥 󰁣󰁯󰁭󰁥󰃧󰁡 󰁡 󰁧󰁩󰁲󰁡󰁲. 󰀱󰀮󰀲󰀮  E󰁳󰁢󰁯󰃧󰁡 󰁯 󰁧󰁲󰃡󰁦󰁩󰁣󰁯 󰁤󰁡 󰁦󰁵󰁮󰃧󰃣󰁯 󰁤 , 󰁰󰁡󰁲󰁡 󰁴 ∈ [0, 75] . I󰁮󰁤󰁩󰁣󰁡 󰁱󰁵󰁡󰁩󰁳 󰁳󰃣󰁯 󰁯󰁳 󰁥󰁸󰁴󰁲󰁥󰁭󰁯󰁳 󰁤󰁡 󰁦󰁵󰁮󰃧󰃣󰁯 󰁥 󰁤󰁡

󰁡󰁮󰃡󰁬󰁩󰁳󰁥 󰁤󰁯 󰁧󰁲󰃡󰁦󰁩󰁣󰁯, 󰁩󰁮󰁤󰁩󰁣󰁡 󰁱󰁵󰁡󰁮󰁴󰁯 󰁴󰁥󰁭󰁰󰁯 󰁤󰁥󰁭󰁯󰁲󰁡 󰁯 M󰁡󰁮󰁵󰁥󰁬 󰁡 󰁤󰁡󰁲 󰁵󰁭󰁡 󰁶󰁯󰁬󰁴󰁡 󰁣󰁯󰁭󰁰󰁬󰁥󰁴󰁡.  ) = 9,5 󰁧󰁲󰁡󰁦󰁩󰁣󰁡󰁭󰁥󰁮󰁴󰁥 , 󰁰 󰁰󰁡󰁲󰁡 󰁡󰁲󰁡 󰁴 ∈ [0, 75] . I󰁮󰁤󰁩󰁣󰁡, 󰁪󰁵󰁳󰁴󰁩󰁦󰁩󰁣󰁡󰁮󰁤󰁯, 󰁱󰁵󰁡󰁮󰁴󰁯 󰀱󰀮󰀳󰀮  R󰁥󰁳󰁯󰁬󰁶󰁥 󰁡 󰁥󰁱󰁵󰁡󰃧󰃣󰁯 󰁤 (󰁴  ) 󰁴󰁥󰁭󰁰󰁯 󰁤󰁥󰁭󰁯󰁲󰁡 󰁯 M󰁡󰁮󰁵󰁥󰁬 󰁡 󰁥󰁮󰁣󰁯󰁮󰁴󰁲󰁡󰁲󰀭󰁳󰁥 󰁰󰁥󰁬󰁡 󰁰󰁲󰁩󰁭󰁥󰁩󰁲󰁡 󰁶󰁥󰁺 󰁡 󰁵󰁭󰁡 󰁤󰁩󰁳󰁴󰃢󰁮󰁣󰁩󰁡 󰁤󰁥 9,5 󰁭󰁥󰁴󰁲󰁯󰁳 󰁤󰁯 󰁳󰁯󰁬󰁯, 󰁤󰁥󰁰󰁯󰁩󰁳 󰁤󰁡 󰁲󰁯󰁤󰁡 󰁧󰁩󰁧󰁡󰁮󰁴󰁥 󰁴󰁥󰁲 󰁣󰁯󰁭󰁥󰃧󰁡󰁤󰁯 󰁡 󰁧󰁩󰁲󰁡󰁲.

󰀲󰀮 

C󰁯󰁮󰁳󰁩󰁤󰁥󰁲󰁡 󰁡 󰁦󰁩󰁧󰁵󰁲󰁡. S󰁡󰁢󰁥󰀭󰁳󰁥 󰁱󰁵󰁥

  󰀽 2   󰀽 4 ; O 󰁰󰁯󰁮󰁴󰁯 P 󰁰󰁥󰁲󰁴󰁥󰁮󰁣󰁥

󰁛ABCD󰁝 󰃩 󰁵󰁭 󰁲󰁥󰁴󰃢󰁮󰁧󰁵󰁬󰁯;

󰁡󰁯 󰁬󰁡󰁤󰁯 󰁛BC󰁝 󰁥 󰁘 󰁤󰁥󰁳󰁩󰁧󰁮󰁡 󰁡 󰁡󰁭󰁰󰁬󰁩󰁴󰁵󰁤󰁥, 󰁥󰁭 󰁲󰁡󰁤󰁩󰁡󰁮󰁯󰁳, 󰁤󰁯 󰃢󰁮󰁧󰁵󰁬󰁯 BAP. BAP . 󰀲󰀮󰀱󰀮  M󰁯󰁳󰁴󰁲󰁥 󰁱󰁵󰁥 󰁡 󰃡󰁲󰁥󰁡 󰁤󰁯 󰁴󰁲󰁩󰃢󰁮󰁧󰁵󰁬󰁯 󰁛PCD󰁝 󰃩 󰁤󰁡󰁤󰁡 󰁰󰁯󰁲 A(󰁸) = 4 󲀓 2 󰁴󰁧 󰁸.

󰁴󰁲󰁩󰃢 󰁮󰁧󰁵󰁬󰁯 󰁛PCD󰁝 󰃩 󰁩󰁧󰁵󰁡󰁬 󰁡 2. 󰀲󰀮󰀲󰀮  D󰁥󰁴󰁥󰁲󰁭󰁩󰁮󰁥 󰁯 󰁶󰁡󰁬󰁯󰁲 󰁤󰁥 󰁸 󰁰󰁡󰁲󰁡 󰁯 󰁱󰁵󰁡󰁬 󰁡 󰃡󰁲󰁥󰁡 󰁤󰁯 󰁴󰁲󰁩󰃢󰁮󰁧󰁵󰁬󰁯 󰀲󰀮󰀳󰀮  S󰁡󰁢󰁥󰁮󰁤󰁯 󰁱󰁵󰁥

 −  󰀽     󰁥 󰁱󰁵󰁥  ∈ 0,  0, . D󰁥󰁴󰁥󰁲󰁭󰁩󰁮󰁥 󰁡 󰃡󰁲󰁥󰁡 󰁤󰁯

󰁴󰁲󰁩󰃢󰁮󰁧󰁵󰁬󰁯 󰁛PCD󰁝 󰁰󰁡󰁲󰁡 󰁸 = α 

󰀳󰀮 

N󰁵󰁭 󰁣󰁥󰁲󰁴󰁯 󰁤󰁩󰁡 󰁡 󰁡󰁬󰁴󰁵󰁲󰁡 󰁤󰁡 󰁭󰁡󰁲󰃩 󰁮󰁵󰁭󰁡 󰁰󰁲󰁡󰁩󰁡 󰃩 󰁤󰁡󰁤󰁡, 󰁡󰁰󰃳󰁳 󰁴 󰁨󰁯󰁲󰁡󰁳, 󰁰󰁯󰁲

ℎ 󰀽 3 +2 + 2  . A

󰁦󰁵󰁮󰃧󰃣󰁯 󰁨 󰁶󰁥󰁭 󰁥󰁭 󰁭󰁥󰁴󰁲󰁯󰁳 󰁥 󰁴∈󰁛0, 24󰁝. 󰁴󰁲 󰁩󰁮󰁴󰁡 󰁭󰁩󰁮󰁵󰁴󰁯󰁳. A 󰁥󰁳󰁳󰁡 󰁨󰁯󰁲󰁡 󰁱󰁵󰁡󰁬 󰁥󰁲󰁡 󰁡 󰁡󰁬󰁴󰁵󰁲󰁡 󰁤󰁡 󰀳󰀮󰀱󰀮  O A󰁬󰁦󰁲󰁥󰁤󰁯 󰁦󰁯󰁩 󰁤󰁡󰁲 󰁵󰁭 󰁭󰁥󰁲󰁧󰁵󰁬󰁨󰁯 󰃠󰁳 󰁮󰁯󰁶󰁥 󰁨󰁯󰁲󰁡󰁳 󰁥 󰁴󰁲󰁩󰁮󰁴󰁡 󰁭󰁡󰁲󰃩? A󰁰󰁲󰁥󰁳󰁥󰁮󰁴󰁡 󰁯 󰁲󰁥󰁳󰁵󰁬󰁴󰁡󰁤󰁯 󰁥󰁭 󰁭󰁥󰁴󰁲󰁯󰁳, 󰁡󰁲󰁲󰁥󰁤󰁯󰁮󰁤󰁡󰁤󰁯 󰃠󰁳 󰁭󰁩󰁬󰃩󰁳󰁩󰁭󰁡󰁳. 󰀳󰀮󰀲󰀮  S󰁥󰁭 󰁵󰁳󰁡󰁲 󰁡 󰁣󰁡󰁬󰁣󰁵󰁬󰁡󰁤󰁯󰁲󰁡 (󰁥󰁸󰁣󰁥󰁴󰁯 󰁰󰁡󰁲󰁡 󰁣󰃡󰁬󰁣󰁵󰁬󰁯󰁳 󰁮󰁵󰁭󰃩󰁲󰁩󰁣󰁯󰁳), 󰁩󰁮󰁤󰁩󰁣󰁡 󰁡󰁰󰃳󰁳 󰁱󰁵󰁡󰁮󰁴󰁯 󰁴󰁥󰁭󰁰󰁯 󰁡 󰁡󰁬󰁴󰁵󰁲󰁡 󰁤󰁡

󰁭󰁡󰁲󰃩 󰁦󰁯󰁩, 󰁰󰁥󰁬󰁡 󰁰󰁲󰁩󰁭󰁥󰁩󰁲󰁡 󰁶󰁥󰁺, 󰁩󰁧󰁵󰁡󰁬 󰁡 4 󰁭󰁥󰁴󰁲󰁯󰁳. 󰀳󰀮󰀳󰀮  E󰁭 󰁱󰁵󰁥 󰁭󰁯󰁭󰁥󰁮󰁴󰁯󰁳 󰁤󰁯 󰁤󰁩󰁡 󰁯󰁣󰁯󰁲󰁲󰁥󰁵 󰁡 󰁰󰁲󰁥󰁩󰁡󰀭󰁭󰁡󰁲 󰁥 󰁡 󰁢󰁡󰁩󰁸󰁡󰀭󰁭󰁡󰁲?

3

Matemática A | 11º Ano | 2013/2014

 

󰀳󰀮󰀴󰀮  R󰁥󰁣󰁯󰁲󰁲󰁥 󰃠 󰁣󰁡󰁬󰁣󰁵󰁬󰁡󰁤󰁯󰁲󰁡 󰁰󰁡󰁲󰁡 󰁤󰁥󰁴󰁥󰁲󰁭󰁩󰁮󰁡󰁲 󰁧󰁲󰁡󰁦󰁩󰁣󰁡󰁭󰁥󰁮󰁴󰁥 (󰁳󰁥 󰁵󰁴󰁩󰁬󰁩󰁺󰁡󰁲󰁥󰁳 󰁶󰁡󰁬󰁯󰁲󰁥󰁳 󰁡󰁰󰁲󰁯󰁸󰁩󰁭󰁡󰁤󰁯󰁳, 󰁵󰁴󰁩󰁬󰁩󰁺󰁡 󰁵󰁭󰁡

󰁡󰁰󰁲󰁯󰁸󰁩󰁭󰁡󰃧󰃣󰁯 󰃠󰁳 󰁤󰃩󰁣󰁩󰁭󰁡󰁳):E󰁭 󰁱󰁵󰁥 󰁰󰁥󰁲󰃭󰁯󰁤󰁯 󰁤󰁯 󰁤󰁩󰁡 󰁯 󰁮󰃭󰁶󰁥󰁬 󰁤󰁡 󰃡󰁧󰁵󰁡 󰁤󰁯 󰁭󰁡󰁲 󰁥󰁳󰁴󰁥󰁶󰁥 󰁡󰁣󰁩󰁭󰁡 󰁤󰁯󰁥 3󰁭 󰁤󰁥 󰁡󰁬󰁴󰁵󰁲󰁡? P󰁲󰁥󰁩󰁡󰀭󰁭󰁡󰁲 (󰁯󰁵  (󰁯󰁵 󰁰󰁲󰁥󰁡󰁭󰁡󰁲) 󰁯󰁵 󰁭󰁡󰁲󰃩 󰁡󰁬󰁴󰁡 󰀭 󰁮󰃭󰁶󰁥󰁬 󰁭󰃡󰁸󰁩󰁭󰁯 󰁤󰁥 󰁵󰁭󰁡 󰁭󰁡󰁲󰃩 󰁣󰁨󰁥󰁩󰁡./B󰁡󰁩󰁸󰁡󰀭󰁭󰁡󰁲 󰁣󰁨󰁥󰁩󰁡./ B󰁡󰁩󰁸󰁡󰀭󰁭󰁡󰁲 󰁯󰁵  󰁯󰁵 󰁭󰁡󰁲󰃩 󰁢󰁡󰁩󰁸󰁡 󰀭 󰁮󰃭󰁶󰁥󰁬 P󰁲󰁥󰁩󰁡󰀭󰁭󰁡󰁲 󰁭󰃭󰁮󰁩󰁭󰁯 󰁤󰁥 󰁵󰁭󰁡 󰁭󰁡󰁲󰃩 󰁶󰁡󰁺󰁡󰁮󰁴󰁥

󰀴󰀮 

C󰁯󰁮󰁳󰁩󰁤󰁥󰁲󰁡 󰁯 󰁣󰃭󰁲󰁣󰁵󰁬󰁯 󰁴󰁲󰁩󰁧󰁯󰁮󰁯󰁭󰃩󰁴󰁲󰁩󰁣󰁯 󰁲󰁥󰁰󰁲󰁥󰁳󰁥󰁮󰁴󰁡󰁤󰁯 󰁮󰁯 󰁲󰁥󰁦󰁥󰁲󰁥󰁮󰁣󰁩󰁡󰁬 󰁯.󰁮. 󰁸O󰁹 󰁤󰁡 󰁦󰁩󰁧󰁵󰁲󰁡. S󰁡󰁢󰁥󰀭󰁳󰁥 󰁱󰁵󰁥 • 

P 󰁥 Q 󰁰󰁥󰁲󰁴󰁥󰁮󰁣󰁥󰁭 󰁡󰁯 󰁣󰃭󰁲󰁣󰁵󰁬󰁯;

• 

 󰀽 ;

• 

A 󰁲󰁥󰁴󰁡 󰁲 󰃩 󰁰󰁡󰁲󰁡󰁬󰁥󰁬󰁡 󰁡 O󰁹 󰁥 󰁩󰁮󰁴󰁥󰁲󰁳󰁥󰁣󰁴󰁡 O󰁸 󰁥󰁭 P;

• 

R 󰃩 󰁯 󰁰󰁯󰁮󰁴󰁯 󰁤󰁥 󰁩󰁮󰁴󰁥󰁲󰁳󰁥󰁣󰃧󰃣󰁯 󰁤󰁡 󰁲󰁥󰁴󰁡 󰁲 󰁣󰁯󰁭 󰁡 󰁳󰁥󰁭󰁩󰁲󰁲󰁥󰁴󰁡

  .

C󰁯󰁮󰁳󰁩󰁤󰁥󰁲󰁡 󰁡󰁩󰁮󰁤󰁡 󰁯 󰁡󰁲󰁣󰁯 RS, 󰁣󰁥󰁮󰁴󰁲󰁡󰁤󰁯 󰁥󰁭 P. I󰁮󰁤󰁩󰁣󰁡 󰁡 󰁡󰁢󰁣󰁩󰁳󰁳󰁡 󰁤󰁯 󰁰󰁯󰁮󰁴󰁯 S (󰁁)  󰁳󰁥󰁮 α 󰀭 󰁴󰁧 α  (󰁂) 1 󲀓 󰁴󰁧 α 

(󰁃) 󰁣󰁯󰁳 α 󰀭 󰁴󰁧 α 

(󰁄) 1 + 󰁴󰁧 α 

2

󰀵󰀮 

  x ) − 3 +  (2 − sen(2x )) . C󰁯󰁮󰁳󰁩󰁤󰁥󰁲󰁡 󰁡 󰁦󰁵󰁮󰃧󰃣󰁯 󰁦 , 󰁲.󰁶.󰁲. 󰁤󰁥󰁦󰁩󰁮󰁩󰁤󰁡 󰁰󰁯󰁲 f (x ) = cos 2 (2

  (2x ) . 󰀵󰀮󰀱󰀮  M󰁯󰁳󰁴󰁲󰁡 󰁱󰁵󰁥 f (x )  = 2 − 4sen 󰀵󰀮󰀲󰀮  D󰁥󰁴󰁥󰁲󰁭󰁩󰁮󰁡: 󰀵󰀮󰀲󰀮󰀱󰀮  󰁯 󰁣󰁯󰁮󰁴󰁲󰁡󰁤󰁯󰁭󰃭󰁮󰁩󰁯 󰁤󰁡 󰁦󰁵󰁮󰃧󰃣󰁯. 󰀵󰀮󰀲󰀮󰀲󰀮 

󰁥󰁸󰁰󰁲󰁥󰁳󰁳󰃣󰁯 󰁧󰁥󰁲󰁡󰁬 󰁤󰁯󰁳 󰁺󰁥󰁲󰁯󰁳 󰁤󰁥 󰁦󰀮 

7 π     5π  󰀵󰀮󰀳󰀮  C󰁡󰁬󰁣󰁵󰁬󰁡 2 f       − 3f   .

 12 

  4  

 󰁣󰁯󰁮󰁪󰁵󰁮󰁴󰁯 󰁘 =  󰀵󰀮󰀴󰀮  󰀮 R󰁥󰁰󰁲󰁥󰁳󰁥󰁮󰁴󰁡 󰁥󰁭 󰁥󰁸󰁴󰁥󰁮󰁳󰃣󰁯 󰁯 󰁣󰁯󰁮󰁪󰁵󰁮󰁴󰁯  x∈ 

󰀵󰀮󰀵󰀮  S󰁡󰁢󰁥󰁮󰁤󰁯 󰁱󰁵󰁥 

󰀶󰀮 

S󰁥

  π sen   − 2

3



4

 ∧ α ∈  0, 2 

; 

π

2 2

  :  f(x)   = 2+2 

2 

.  

π   , 󰁤󰁥󰁴󰁥󰁲󰁭󰁩󰁮󰁡 󰁯 󰁶󰁡󰁬󰁯󰁲 󰁥󰁸󰁡󰁴󰁯 󰁤󰁥 f (α   ).

‖‖ 󰀽  󰀽   󰀽 1 󰁥   󰁰󰁥󰁲󰁰󰁥󰁮󰁤󰁩󰁣󰁵󰁬󰁡󰁲 󰁡  , 󰁥󰁮󰁴󰃣󰁯 2  + 4  . −  +  󰃩 󰁩󰁧󰁵󰁡󰁬 󰁡 (󰁁) 1

󰀷󰀮 

  + 2α =  



π

(󰁂) −2

(󰁃) 󰀭2

(󰁄) 1

∈

+

∈

C󰁯󰁮󰁳󰁩󰁤󰁥󰁲󰁥󰁭󰁯󰁳 󰁯󰁳 󰁶󰁥󰁴󰁯󰁲󰁥󰁳 󰁶  (2  (2󰁡,󰁢) 󰁥 󰁷  (−  (− 󰁢,󰁡), 󰁣󰁯󰁭 󰁡 IR  󰁥 󰁢  IR 󰁜󰁻0󰁽. O 󰃢󰁮󰁧󰁵󰁬󰁯 󰁦󰁯󰁲󰁭󰁡󰁤󰁯 󰁥󰁮󰁴󰁲󰁥 󰁡󰁭󰁢󰁯󰁳 󰁯󰁳 󰁶󰁥󰁴󰁯󰁲󰁥󰁳 󰃩

(󰁁) 󰁡󰁧󰁵󰁤󰁯 󰁳󰁥 󰁢0

(󰁃) 󰁯󰁢󰁴󰁵󰁳󰁯 󰁳󰁥 󰁢