85
punti
Livello 1
SIN(pi/6 - ACOS(- 1/3))=
=SIN(pi/6)·COS(ACOS(- 1/3)) - SIN(ACOS(- 1/3))·COS(pi/6)=
=1/2·(- 1/3) - SIN(ACOS(- 1/3))·(√3/2)=
(SIN(α) = √(1 - (- 1/3)^2)= 2·√2/3)
=1/2·(- 1/3) - 2·√2/3·(√3/2)=
=- √6/3 - 1/6= - (2·√6 + 1)/6
90143
punti
Genius II
* sin(a - b) = sin(a)*cos(b) - sin(b)*cos(a)
con
* a = π/6 = 30°; sin(a) = 1/2; cos(a) = √3/2;
* b = arccos(- 1/3) ~= 110°; sin(b) = 2*√2/3; cos(b) = - 1/3;
si ha
* sin(π/6 - arccos(- 1/3)) = (1/2)*(- 1/3) - (2*√2/3)*(√3/2) = - (1 + 2*√6)/6
* arcsin(- (1 + 2*√6)/6) ~= - 80°
57171
punti
Genius I