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

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

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

± π 6 + 2 π n , n ϵ Z \pm\frac{\pi}{6}\ +2\pi n,\ n\ \epsilon\ Z ± 6 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 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 n ; n ϵ Z \pi n;\ n\ \epsilon\ Z 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

Решить уравнение sin ⁡ x = 0 \sin x\ =\ 0 sin x = 0

π n , n ϵ Z \pi n,\ n\ \epsilon\ Z π n , n ϵ Z

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

Решить уравнение sin ⁡ x = 1 \sin x\ =\ 1 sin x = 1

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

π n , n ϵ Z \pi n,\ n\ \epsilon\ Z π n , n ϵ Z

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

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

Решить уравнение sin ⁡ x = − 1 \sin x\ =-\ 1 sin x = − 1

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

π n , n ϵ Z \pi n,\ n\ \epsilon\ Z π n , n ϵ Z

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

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

Решить уравнение sin ⁡ x = 1 7 \sin x\ =\frac{1}{7} sin x = 7 1

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

Решить уравнение sin ⁡ x = − 5 6 \sin x\ =-\frac{5}{6} sin x = − 6 5

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

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

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

Решить уравнение sin ⁡ x = 6 5 \sin x\ =\frac{6}{5} sin x = 5 6

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

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

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

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

± 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

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 ; n ϵ Z \pm\frac{\pi}{6}\ +2\pi n;\ n\ \epsilon\ Z ± 6 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 cos ⁡ x = − 3 2 \cos x\ =-\ \frac{\sqrt{3}}{2} cos 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">

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

± π 6 + 2 π n ; n ϵ Z \pm\frac{\pi}{6}\ +2\pi n;\ \ n\ \epsilon\ Z ± 6 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 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 cos ⁡ x = 0 \cos x\ =0 cos x = 0

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

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

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

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

Решить уравнение cos ⁡ x = 1 \cos x\ =1 cos x = 1

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

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

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

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

Решить уравнение cos ⁡ x = − 1 \cos x\ =-\ 1 cos x = − 1

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

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

Решить уравнение cos ⁡ x = 0 , 8 \cos x\ =0,8 cos x = 0 , 8

± arccos ⁡ 0 , 8 + 2 π n ; n ϵ Z \pm\arccos0,8\ +2\pi n;\ \ n\ \epsilon\ Z ± arccos 0 , 8 + 2 π n ; n ϵ Z

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

arccos ⁡ 0 , 8 + π n ; n ϵ Z \arccos0,8\ +\pi n;\ \ n\ \epsilon\ Z arccos 0 , 8 + π n ; n ϵ Z

Решить уравнение t g x = 1 tgx\ =1 t g x = 1

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

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

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

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

Решить уравнение t g x = 3 tgx\ =\sqrt{3} 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">

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

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

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

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

Решить уравнение t g x = 1 3 tgx\ =\frac{1}{\sqrt{3}} 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

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

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

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

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

Решить уравнение t g x = − 1 tgx\ =-1 t g x = − 1

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

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

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

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

Решить уравнение t g x = 0 tgx\ =0 t g x = 0

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

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

Решить уравнение t g x = 10 tgx\ =10 t g x = 1 0

a r ctg ⁡ 10 + π n ; n ϵ Z ar\operatorname{ctg}10+\pi n;\ \ n\ \epsilon\ Z a r c t g 1 0 + π n ; n ϵ Z

− a r ctg ⁡ 10 + π n ; n ϵ Z -\ ar\operatorname{ctg}10+\pi n;\ \ n\ \epsilon\ Z − a r c t g 1 0 + π n ; n ϵ Z

a r ctg ⁡ 10 + 2 π n ; n ϵ Z ar\operatorname{ctg}10+2\pi n;\ \ n\ \epsilon\ Z a r c t g 1 0 + 2 π n ; n ϵ Z

− a r ctg ⁡ 10 + 2 π n ; n ϵ Z -\ ar\operatorname{ctg}10+2\pi n;\ \ n\ \epsilon\ Z − a r c t g 1 0 + 2 π n ; n ϵ Z

Решить уравнение ctg ⁡ x = − 1 \operatorname{ctg}x\ =-1 c t g x = − 1

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

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

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

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

Решить уравнение ctg ⁡ x = 3 \operatorname{ctg}x\ =\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">

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

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

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

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

Решить уравнение ctg ⁡ x = 0 \operatorname{ctg}x\ =0 c t g x = 0

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

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

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

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

Решить 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

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

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

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

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

Простейшие тригонометрические уравнения

Authored by Beniamin Kazarov

Mathematics

10th - 11th Grade

Used 57+ times

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Решить уравнение
$\sin x\ =\frac{1}{7}$

$\arcsin\frac{1}{7}\ +2\pi n;\ \ \pi\ -\ \arcsin\frac{1}{7}\ +2\pi n;\ n\ \epsilon\ Z$

решений нет

$-\arcsin\frac{1}{7}\ +2\pi n;\ \ -\ \pi\ +\ \arcsin\frac{1}{7}\ +2\pi n;\ n\ \epsilon\ Z$

$\frac{\pi}{2}\ +\pi n,\ n\ \epsilon\ Z$

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Простейшие тригонометрические уравнения

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

Решить уравнение sin⁡x = 22\sin x\ =\ \frac{\sqrt{2}}{2}sinx = 22​​

Решить уравнение sin⁡x = 32\sin x\ =\ \frac{\sqrt{3}}{2}sinx = 23​​

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

Решить уравнение sin⁡x = −22\sin x\ =\ -\frac{\sqrt{2}}{2}sinx = −22​​

Решить уравнение sin⁡x = −32\sin x\ =\ -\frac{\sqrt{3}}{2}sinx = −23​​

Решить уравнение sin⁡x = 0\sin x\ =\ 0sinx = 0

Решить уравнение sin⁡x = 1\sin x\ =\ 1sinx = 1

Решить уравнение sin⁡x =− 1\sin x\ =-\ 1sinx =− 1

Решить уравнение sin⁡x =17\sin x\ =\frac{1}{7}sinx =71​

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