Предмет: Алгебра, автор: sverchenina

Найдите угол a, если a∈[0;2\pi] и выполняется условие: sin²\frac{a}{4}-cos²\frac{a}{4}=\frac{1}{2}

Ответы

Автор ответа: iosiffinikov
0

Ответ:

а=120 градусов  или, в радианах, а=2pi/3

Объяснение:

sin²(а/4)-cos²(а/4)=0,5

-cos(а/2)=0,5

а/2=5pi/3+2*pi*n

или

а/2=7pi/3+2*pi*n

где n -любое целое

значит  а=10pi/3+4*pi*n

или

значит  а=14pi/3+4*pi*n

в заданный интервал попадает

а=(14/3-4)*pi=2pi/3

или а=120 градусов

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