Укажите решение уравнения cos ⁡ x = − 1 \cos x=-1 cos x = − 1

π + 2 π n \pi+2\pi n π + 2 π n

− π 2 + 2 π n -\frac{\pi}{2}+2\pi n − 2 π + 2 π n

± π + π n \pm\pi+\pi n ± π + π n

Решите уравнение ctg ⁡ x = 1 3 \operatorname{ctg}x=\frac{1}{\sqrt{3}} c t g x = 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 1

x = π 3 + π k x=\frac{\pi}{3}+\pi k x = 3 π + π k

x = 7 π 6 + π n x=\frac{7\pi}{6}+\pi n x = 6 7 π + π n

x = π 6 + π k x=\frac{\pi}{6}+\pi k x = 6 π + π k

x = π 3 + 2 π k x=\frac{\pi}{3}+2\pi k x = 3 π + 2 π k

Решите уравнение cos ⁡ x = 1 2 \cos x=\frac{1}{2} cos x = 2 1

x = ± π 3 + 2 π k x=\pm\frac{\pi}{3}+2\pi k x = ± 3 π + 2 π k

x = − π 3 + 2 π n x=-\frac{\pi}{3}+2\pi n x = − 3 π + 2 π n

x = ± π 3 + π n x=\pm\frac{\pi}{3}+\pi n x = ± 3 π + π n

x = π 3 + 2 π n x=\frac{\pi}{3}+2\pi n x = 3 π + 2 π n

Выберите все решения уравнения sin ⁡ x = 3 2 \sin x=\frac{\sqrt{3}}{2} sin x = 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

x = π 3 + 2 π n x=\frac{\pi}{3}+2\pi n x = 3 π + 2 π n

x = 2 π 3 + 2 π n x=\frac{2\pi}{3}+2\pi n x = 3 2 π + 2 π n

x = − π 3 + 2 π n x=-\frac{\pi}{3}+2\pi n x = − 3 π + 2 π n

Решите уравнение cos ⁡ x = 1 2 \cos x=\frac{1}{2} cos x = 2 1

x = π 3 + 2 π n x=\frac{\pi}{3}+2\pi n x = 3 π + 2 π n

x = − π 3 + 2 π n x=-\frac{\pi}{3}+2\pi n x = − 3 π + 2 π n

x = 2 π 3 + 2 π n x=\frac{2\pi}{3}+2\pi n x = 3 2 π + 2 π n

Решите уравнение 2 sin ⁡ x = 4 2\sin x=4 2 sin x = 4

x = ( − 1 ) k ⋅ π 6 + π k x=\left(-1\right)^k\cdot\frac{\pi}{6}+\pi k x = ( − 1 ) k ⋅ 6 π + π k

x = arcsin ⁡ 2 + 2 π k x=\arcsin2+2\pi k x = arcsin 2 + 2 π k

x = ( − 1 ) n arcsin ⁡ 2 + 2 π n x=\left(-1\right)^n\arcsin2+2\pi n x = ( − 1 ) n arcsin 2 + 2 π n

Тригонометрические уравнения

Authored by Марина Геннадьевна

Mathematics

10th - 11th Grade

CCSS covered

Used 407+ times

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MULTIPLE CHOICE QUESTION

10 sec • 1 pt

Укажите решение уравнения $\cos x=-1$

$2\pi n$

$-\frac{\pi}{2}+2\pi n$

$\pi+2\pi n$

$\pm\pi+\pi n$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

Укажите формулу для решения уравнения tgx=a

$x=\pm ar\operatorname{ctg}a+\pi n$

$x=\pm ar\operatorname{ctg}a+2\pi n$

$x=ar\operatorname{ctg}a+2\pi n$

$x=ar\operatorname{ctg}a+\pi n$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

Укажите формулу для решения уравнения sinx=0

$x=\frac{\pi}{2}+\pi n$

$x=\frac{\pi}{2}+2\pi n$

$x=\pi n$

$x=2\pi n$

Tags

CCSS.HSF.TF.B.7

MULTIPLE SELECT QUESTION

20 sec • 1 pt

Укажите все формулы для решения уравнения cosx=a

$x=\arccos a+2\pi n$

$x=\pi-\arccos a+2\pi n$

$x=-\arccos a+2\pi n$

$x=-\arccos a+\pi n$

Tags

CCSS.HSF.TF.B.7

MULTIPLE SELECT QUESTION

20 sec • 1 pt

Укажите все формулы для решения уравнения sinx=a

$x=\arcsin x+2\pi n$

$x=\arcsin a+2\pi n$

$x=\pi-\arcsin a+\pi n$

$x=\pi-\arcsin a+2\pi n$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Решите уравнение $\operatorname{ctg}x=\frac{1}{\sqrt{3}}$

$x=\frac{7\pi}{6}+\pi n$

$x=\frac{\pi}{3}+\pi k$

$x=\frac{\pi}{6}+\pi k$

$x=\frac{\pi}{3}+2\pi k$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Решите уравнение $\cos x=\frac{1}{2}$

$x=-\frac{\pi}{3}+2\pi n$

$x=\pm\frac{\pi}{3}+\pi n$

$x=\frac{\pi}{3}+2\pi n$

$x=\pm\frac{\pi}{3}+2\pi k$

Tags

CCSS.HSF.TF.B.7

MULTIPLE SELECT QUESTION

20 sec • 1 pt

Выберите все решения уравнения $\sin x=\frac{\sqrt{3}}{2}$

$x=\frac{2\pi}{3}+2\pi n$

$x=\frac{\pi}{3}+2\pi n$

$x=-\frac{\pi}{3}+2\pi n$

Tags

CCSS.HSF.TF.B.7

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Решите уравнение $\cos x=\frac{1}{2}$

$x=\frac{2\pi}{3}+2\pi n$

$x=\frac{\pi}{3}+2\pi n$

$x=\pi n$

$x=-\frac{\pi}{3}+2\pi n$

Tags

CCSS.HSF.TF.B.7

10.

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Решите уравнение $2\sin x=4$

$x=\left(-1\right)^k\cdot\frac{\pi}{6}+\pi k$

$x=\arcsin2+2\pi k$

$x=\left(-1\right)^n\arcsin2+2\pi n$

нет решений

Tags

CCSS.HSF.TF.B.7

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Тригонометрические уравнения

Укажите решение уравнения cos⁡x=−1\cos x=-1cosx=−1

Укажите формулу для решения уравнения tgx=a

Укажите формулу для решения уравнения sinx=0

Укажите все формулы для решения уравнения cosx=a

Укажите все формулы для решения уравнения sinx=a

Решите уравнение ctg⁡x=13\operatorname{ctg}x=\frac{1}{\sqrt{3}}ctgx=3​1​

Решите уравнение cos⁡x=12\cos x=\frac{1}{2}cosx=21​

Выберите все решения уравнения sin⁡x=32\sin x=\frac{\sqrt{3}}{2}sinx=23​​

Решите уравнение cos⁡x=12\cos x=\frac{1}{2}cosx=21​

Решите уравнение 2sin⁡x=42\sin x=42sinx=4

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Popular Resources on Wayground

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Укажите решение уравнения $\cos x=-1$

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Решите уравнение $\cos x=\frac{1}{2}$

Решите уравнение $2\sin x=4$