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">

x = − π 6 + 2 k π ∨ x = π 6 + 2 k π x=-\frac{\pi}{6}+2k\pi\ \vee\ x=\frac{\pi}{6}+2k\pi x = − 6 π + 2 k π ∨ x = 6 π + 2 k π

x = − π 3 + 2 k π ∨ x = π 3 + 2 k π x=-\frac{\pi}{3}+2k\pi\ \vee\ x=\frac{\pi}{3}+2k\pi x = − 3 π + 2 k π ∨ x = 3 π + 2 k π

x = π 4 + 2 k π ∨ x = − π 4 + 2 k π x=\frac{\pi}{4}+2k\pi\ \vee\ x=-\frac{\pi}{4}+2k\pi x = 4 π + 2 k π ∨ x = − 4 π + 2 k π

x = 2 π 3 + 2 k π ∨ x = − π 3 + 2 k π x=\frac{2\pi}{3}+2k\pi\ \vee\ x=-\frac{\pi}{3}+2k\pi x = 3 2 π + 2 k π ∨ x = − 3 π + 2 k π

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

x = π 6 + 2 k π ∨ x = 5 6 π + 2 k π x=\frac{\pi}{6}+2k\pi\ \vee\ x=\frac{5}{6}\pi+2k\pi x = 6 π + 2 k π ∨ x = 6 5 π + 2 k π

d x = − π 4 + 2 k π ∨ x = 3 π 4 + 2 k π x=-\frac{\pi}{4}+2k\pi\ \vee\ x=\frac{3\pi}{4}+2k\pi x = − 4 π + 2 k π ∨ x = 4 3 π + 2 k π

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

x = − π 3 + 2 k π ∨ x = π 3 + 2 k π x=-\frac{\pi}{3}+2k\pi\ \vee\ x=\frac{\pi}{3}+2k\pi x = − 3 π + 2 k π ∨ x = 3 π + 2 k π

sin ⁡ ( x ) = − 2 2 \sin\left(x\right)=-\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">

x = − π 4 + 2 k π ∨ x = 5 π 4 + 2 k π x=-\frac{\pi}{4}+2k\pi\ \vee\ x=\frac{5\pi}{4}+2k\pi x = − 4 π + 2 k π ∨ x = 4 5 π + 2 k π

x = − π 4 + 2 k π ∨ x = π 4 + 2 k π x=-\frac{\pi}{4}+2k\pi\ \vee\ x=\frac{\pi}{4}+2k\pi x = − 4 π + 2 k π ∨ x = 4 π + 2 k π

x = − π 4 + 2 k π ∨ x = 3 π 4 + 2 k π x=-\frac{\pi}{4}+2k\pi\ \vee\ x=\frac{3\pi}{4}+2k\pi x = − 4 π + 2 k π ∨ x = 4 3 π + 2 k π

x = − π 3 + 2 k π ∨ x = π 3 + 2 k π x=-\frac{\pi}{3}+2k\pi\ \vee\ x=\frac{\pi}{3}+2k\pi x = − 3 π + 2 k π ∨ x = 3 π + 2 k π

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">

x = 5 π 6 + 2 k π ∨ x = 7 π 6 + 2 k π x=\frac{5\pi}{6}+2k\pi\ \vee\ x=\frac{7\pi}{6}+2k\pi x = 6 5 π + 2 k π ∨ x = 6 7 π + 2 k π

x = − π 3 + 2 k π ∨ x = π 3 + 2 k π x=-\frac{\pi}{3}+2k\pi\ \vee\ x=\frac{\pi}{3}+2k\pi x = − 3 π + 2 k π ∨ x = 3 π + 2 k π

x = − π 4 + 2 k π ∨ x = 5 π 4 + 2 k π x=-\frac{\pi}{4}+2k\pi\ \vee\ x=\frac{5\pi}{4}+2k\pi x = − 4 π + 2 k π ∨ x = 4 5 π + 2 k π

x = − 2 π 3 + 2 k π ∨ x = 4 π 3 + 2 k π x=-\frac{2\pi}{3}+2k\pi\ \vee\ x=\frac{4\pi}{3}+2k\pi x = − 3 2 π + 2 k π ∨ x = 3 4 π + 2 k π

sin ⁡ x = 1 \sin x=1 sin x = 1

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

x = π 2 k x=\frac{\pi}{2}k\ x = 2 π k

cos ⁡ x = − 1 \cos x=-1 cos x = − 1

x = π + 2 k π x=\pi+2k\pi\ x = π + 2 k π

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

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

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">

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

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

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

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

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

x = − π 4 + k π x=-\frac{\pi}{4}+k\pi\ x = − 4 π + k π

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

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

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

t g x = − 3 3 tgx=-\frac{\sqrt{3}}{3} t g x = − 3 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 6 + k π x=-\frac{\pi}{6}+k\pi\ x = − 6 π + k π

x = − π 4 + k π x=-\frac{\pi}{4}+k\pi\ x = − 4 π + k π

x = − π 6 + 2 k π x=-\frac{\pi}{6}+2k\pi\ x = − 6 π + 2 k π

x = − π 6 + k π ∨ x = π 6 + k π x=-\frac{\pi}{6}+k\pi\ \ \vee\ x=\frac{\pi}{6}+k\pi\ x = − 6 π + k π ∨ x = 6 π + k π

Równania trygonometryczne

Mathematics

11th Grade

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$\sin^2x=\frac{1}{2}$

$x=-\frac{\pi}{4}+\frac{k\pi}{2}\$

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

$x=\frac{\pi}{6}+\frac{k\pi}{2}\$

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

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Równania trygonometryczne

cos⁡x=32\cos x=\frac{\sqrt{3}}{2}cosx=23​​

sin⁡x=12\sin x=\frac{1}{2}sinx=21​

sin⁡(x)=−22\sin\left(x\right)=-\frac{\sqrt{2}}{2}sin(x)=−22​​

cos⁡x=−32\cos x=-\frac{\sqrt{3}}{2}cosx=−23​​

sin⁡x=1\sin x=1sinx=1

cos⁡x=−1\cos x=-1cosx=−1

tgx=3tgx=\sqrt{3}tgx=3​

ctg⁡x=−1\operatorname{ctg}x=-1ctgx=−1

tgx=−33tgx=-\frac{\sqrt{3}}{3}tgx=−33​​

sin⁡2x=12\sin^2x=\frac{1}{2}sin2x=21​

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$\cos x=\frac{\sqrt{3}}{2}$

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