[Risolto] Formule goniometriche

Identità utili
* sin(arcsin(x)) = x
* cos(arcsin(x)) = √(1 - x^2)
* sin(2*x) = 2*cos(x)*sin(x)
* cos(2*x) = cos^2(x) - sin^2(x)
* sin(π - x) = sin(x)
* cos(π - x) = - cos(x)
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Determinare le funzioni goniometriche dell'angolo AĈB
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* sin(π - 2*arcsin(1/4)) = sin(2*arcsin(1/4)) =
= 2*cos(arcsin(1/4))*sin(arcsin(1/4)) =
= 2*(√(1 - (1/4)^2))*(1/4) =
= √15/8
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* cos(π - 2*arcsin(1/4)) = - cos(2*arcsin(1/4)) =
= sin^2(arcsin(1/4)) - cos^2(arcsin(1/4)) =
= (1/4)^2 - (1 - (1/4)^2) =
= - 7/8

α = β = ASIN(1/4)

SIN(α) = SIN(β) = 1/4

SIN(α) = 1/4-----> α = 14.48 ° circa

quindi: 

γ = 180 - 2·14.48  = 151.04° (circa)

Angolo ottuso (2° quadrante)

SIN(γ) = SIN(pi - 2·α)----> SIN(γ) = SIN(2·α)

SIN(γ) = 2·SIN(α)·COS(α)

con: SIN(α) = 1/4; COS(α) = √(1 - (1/4)^2)= √15/4

SIN(γ) = 2·1/4·(√15/4)----> SIN(γ) = √15/8

COS(γ) = - √(1 - (√15/8)^2)------> COS(γ) = - 7/8

TAN(γ) = SIN(γ)/COS(γ)= √15/8/(- 7/8)----> TAN(γ) = - √15/7

COT(γ) = - 7/√15----> COT(γ) = - 7·√15/15