Найдите корни уравнения tgx+1=0, принадлежащие отрезку [0;2П]. Created by RussMan. matematika-ru

Найдите корни уравнения tgx+1=0, принадлежащие отрезку [0;2П]...

June 2022 2 16 Report

Найдите корни уравнения tgx+1=0, принадлежащие отрезку [0;2П]

m11m

Verified answer

Tgx+1=0
tgx=-1
x=-π/4 + πn, n∈Z

На отрезке [0; 2π]:
0≤ -π/4 +πn ≤2π
π/4 ≤ πn ≤ 2π +π/4
π/4 ≤ πn ≤ 9π/4
1/4 ≤ n ≤ 9/4
n=1; 2

При n=1 x=-π/4 +π =3π/4
n=2 x=-π/4 +2π = 7π/4

Ответ: 3π/4; 7π/4.

4 votes Thanks 8

julyap

Verified answer

$tgx+1=0\\tgx=-1\\x=- \frac{ \pi }{4} + \pi n\\\\n=1\\x=- \frac{ \pi }{4} + \pi = \frac{- \pi +4 \pi }{4} = \frac{3 \pi }{4} \\ n=2\\x=- \frac{ \pi }{4} +2 \pi = \frac{- \pi +8 \pi }{4} = \frac{7 \pi }{4}$

$n=1\\n=2$

2 votes Thanks 6

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