Предмет: Алгебра, автор: markinner

решите тригонометрическое неравенство tg t<=1

Ответы

Автор ответа: Удачник66

1

Ответ:

t ∈ (-pi/2 + pi*k; pi/4 + pi*k]

Объяснение:

Вот на рисунке показан примерный график y = tg x.

Извините, нарисовано кривовато, но Пайнт точнее рисовать не может.

Как известно, решением уравнения tg x = 1 будет x = pi/4 + pi*k.

А при x = -pi/2 + pi*k будет tg x = -oo (то есть не определен).

Поэтому решением неравенства

tg t <= 1

является промежуток

t ∈ (-pi/2 + pi*k; pi/4 + pi*k]

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