Задача 10754 Найдите значение выражения...

slava191

23.10.2016

Найдите значение выражения sin^2(5Pi/3)/sin^2(5Pi/4)

SOVA

23.10.2016

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sin(5π/3)=sin((6π-π)/3)=sin(2π-(π/3))=-sin(π/3)
sin^2(5π/3)=(-sin(π/3))^2=(-sqrt(3)/2)^2=3/4
sin(5π/4)=sin((4π+π)/4)=sin(π+(π/4))=-sin(π/4)
sin^2(5π/4)=(-sin(π/4))^2=(-sqrt(2)/2)^2=2/4

sin^2(5π/3)/sin^2(5π/4)=(3/4)/(2/4)=3/2=1,5