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

Решить уравнение sin ⁡ x = 1 2 \sin x\ =\ \frac{1}{2} sin x = 2 1

π 6 + 2 π n ; 5 π 6 + 2 π n ; n ϵ Z \frac{\pi}{6}\ +2\pi n;\ \frac{5\pi}{6}\ +2\pi n;\ n\ \epsilon\ Z 6 π + 2 π n ; 6 5 π + 2 π n ; n ϵ Z

π 3 + 2 π n ; 2 π 3 + 2 π n ; n ϵ Z \frac{\pi}{3}\ +2\pi n;\ \frac{2\pi}{3}\ +2\pi n;\ n\ \epsilon\ Z 3 π + 2 π n ; 3 2 π + 2 π n ; n ϵ Z

− π 6 + 2 π n ; − 5 π 6 + 2 π n ; n ϵ Z -\frac{\pi}{6}\ +2\pi n;\ -\frac{5\pi}{6}\ +2\pi n;\ n\ \epsilon\ Z − 6 π + 2 π n ; − 6 5 π + 2 π n ; n ϵ Z

− π 3 + 2 π n ; − 2 π 3 + 2 π n ; n ϵ Z -\frac{\pi}{3}\ +2\pi n;\ -\frac{2\pi}{3}\ +2\pi n;\ n\ \epsilon\ Z − 3 π + 2 π n ; − 3 2 π + 2 π n ; n ϵ Z

Решить уравнение sin ⁡ x = 2 2 \sin x\ =\ \frac{\sqrt{2}}{2} sin x = 2 2 <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">

π 4 + 2 π n ; 3 π 4 + 2 π n ; n ϵ Z \frac{\pi}{4}\ +2\pi n;\ \frac{3\pi}{4}\ +2\pi n;\ n\ \epsilon\ Z 4 π + 2 π n ; 4 3 π + 2 π n ; n ϵ Z

π 3 + 2 π n ; 2 π 3 + 2 π n ; n ϵ Z \frac{\pi}{3}\ +2\pi n;\ \frac{2\pi}{3}\ +2\pi n;\ n\ \epsilon\ Z 3 π + 2 π n ; 3 2 π + 2 π n ; n ϵ Z

− π 4 + 2 π n ; − 3 π 4 + 2 π n ; n ϵ Z -\frac{\pi}{4}\ +2\pi n;\ -\frac{3\pi}{4}\ +2\pi n;\ n\ \epsilon\ Z − 4 π + 2 π n ; − 4 3 π + 2 π n ; n ϵ Z

± π 4 + 2 π n , n ϵ Z \pm\frac{\pi}{4}\ +2\pi n,\ n\ \epsilon\ Z ± 4 π + 2 π n , n ϵ Z

Решить уравнение 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">

π 3 + 2 π n ; 2 π 3 + 2 π n ; n ϵ Z \frac{\pi}{3}\ +2\pi n;\ \frac{2\pi}{3}\ +2\pi n;\ n\ \epsilon\ Z 3 π + 2 π n ; 3 2 π + 2 π n ; n ϵ Z

− π 3 + 2 π n ; − 2 π 3 + 2 π n ; n ϵ Z -\frac{\pi}{3}\ +2\pi n;\ -\frac{2\pi}{3}\ +2\pi n;\ n\ \epsilon\ Z − 3 π + 2 π n ; − 3 2 π + 2 π n ; n ϵ Z

2 π n ; n ϵ Z 2\pi n;\ n\ \epsilon\ Z 2 π n ; n ϵ Z

± π 3 + 2 π n , n ϵ Z \pm\frac{\pi}{3}\ +2\pi n,\ n\ \epsilon\ Z ± 3 π + 2 π n , n ϵ Z

простейшие тригонометрические уравнения

Authored by Гузель Мингазова

Mathematics

5th Grade

CCSS covered

Used 11+ times

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12 questions

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MULTIPLE CHOICE QUESTION

30 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

30 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

30 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

30 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

30 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

30 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

30 sec • 1 pt

Решить уравнение
$\sin x\ =\ \frac{1}{2}$

$\frac{\pi}{6}\ +2\pi n;\ \frac{5\pi}{6}\ +2\pi n;\ n\ \epsilon\ Z$

$\frac{\pi}{3}\ +2\pi n;\ \frac{2\pi}{3}\ +2\pi n;\ n\ \epsilon\ Z$

$-\frac{\pi}{6}\ +2\pi n;\ -\frac{5\pi}{6}\ +2\pi n;\ n\ \epsilon\ Z$

$-\frac{\pi}{3}\ +2\pi n;\ -\frac{2\pi}{3}\ +2\pi n;\ n\ \epsilon\ Z$

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простейшие 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​

Решить уравнение sin⁡x = 12\sin x\ =\ \frac{1}{2}sinx = 21​

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Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Укажите решение уравнения $\cos x=-1$

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

Решите уравнение $\cos x=\frac{1}{2}$

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

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