cos ⁡ ( 3 π 2 − α ) \cos\left(\frac{3\pi}{2}-\alpha\right) cos ( 2 3 π − α )

− sin ⁡ α -\sin\alpha − sin α

− cos ⁡ α -\cos\alpha − cos α

cos ⁡ ( 3 π 2 − α ) \cos\left(\frac{3\pi}{2}-\alpha\right) cos ( 2 3 π − α )

− sin ⁡ α -\sin\alpha − sin α

− cos ⁡ α -\cos\alpha − cos α

t g ( π 2 − α ) tg\left(\frac{\pi}{2}-\alpha\right) t g ( 2 π − α )

ctg ⁡ α \operatorname{ctg}\alpha c t g α

− t g α -tg\alpha − t g α

− ctg ⁡ α -\operatorname{ctg}\alpha − c t g α

cos ⁡ π 4 \cos\ \frac{\pi}{4} cos 4 π

2 2 \frac{\sqrt{2}}{2} 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">

3 2 \frac{\sqrt{3}}{2} 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">

a r ctg ⁡ 3 ar\operatorname{ctg}\sqrt{3} a r c t g 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 -\frac{\pi}{3} − 3 π

sin ⁡ 3 0 o \sin\ 30^o sin 3 0 o

2 2 \frac{\sqrt{2}}{2} 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">

3 2 \frac{\sqrt{3}}{2} 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">

sin ⁡ 4 5 o \sin\ 45^o sin 4 5 o

2 2 \frac{\sqrt{2}}{2} 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">

3 2 \frac{\sqrt{3}}{2} 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">

sin ⁡ 6 0 o \sin\ 60^o sin 6 0 o

3 2 \frac{\sqrt{3}}{2} 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">

2 2 \frac{\sqrt{2}}{2} 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">

cos ⁡ 6 0 o \cos\ 60^o cos 6 0 o

2 2 \frac{\sqrt{2}}{2} 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">

3 2 \frac{\sqrt{3}}{2} 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">

Нахождение синуса тупого угла:

sin ⁡ ( 18 0 o − α ) = sin ⁡ α \sin\ \left(180^o-\alpha\right)=\sin\ \alpha sin ( 1 8 0 o − α ) = sin α

sin ⁡ ( 18 0 o + α ) = sin ⁡ α \sin\ \left(180^o+\alpha\right)=\sin\ \alpha sin ( 1 8 0 o + α ) = sin α

sin ⁡ ( 18 0 o − α ) = − sin ⁡ α \sin\ \left(180^o-\alpha\right)=-\sin\ \alpha sin ( 1 8 0 o − α ) = − sin α

sin ⁡ ( 18 0 o − α ) = cos ⁡ α \sin\ \left(180^o-\alpha\right)=\cos\ \alpha sin ( 1 8 0 o − α ) = cos α

тригонометрия

Authored by Лана Лашкевич

Mathematics

11th Grade

Used 5+ times

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24 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

основное тригонометрическое тождество

$\sin^2x\ +\cos^2x=1$

$1+tg^2x=\frac{1}{\cos^2x}$

$\sin^2x+\cos^2y=1$

$tgx\times\operatorname{ctg}x=1$

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

$\sin2x=$

$\cos^2x-\sin^2x$

$2\sin x\cos x$

$\sin x\cos x$

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

$\cos\left(\frac{3\pi}{2}-\alpha\right)$

$\sin\alpha$

$\cos\alpha$

$-\sin\alpha$

$-\cos\alpha$

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

$\cos\left(\frac{3\pi}{2}-\alpha\right)$

$\sin\alpha$

$\cos\alpha$

$-\sin\alpha$

$-\cos\alpha$

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

$tg\left(\frac{\pi}{2}-\alpha\right)$

$-tg\alpha$

$\operatorname{ctg}\alpha$

$tg\alpha$

$-\operatorname{ctg}\alpha$

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

$\cos\ \frac{\pi}{4}$

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{\sqrt{2}}{2}$

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

$ar\operatorname{ctg}\sqrt{3}$

$\frac{\pi}{3}$

$\frac{4\pi}{3}$

$\frac{\pi}{6}$

$-\frac{\pi}{3}$

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

Найдите $\arcsin\left(-\frac{\pi}{2}\right)$

-1

не существует

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

Существует ли такой угол, для которого $\sin\alpha=-\sqrt{3}$

да

нет

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тригонометрия

основное тригонометрическое тождество

sin⁡2x=\sin2x=sin2x=

cos⁡(3π2−α)\cos\left(\frac{3\pi}{2}-\alpha\right)cos(23π​−α)

cos⁡(3π2−α)\cos\left(\frac{3\pi}{2}-\alpha\right)cos(23π​−α)

tg(π2−α)tg\left(\frac{\pi}{2}-\alpha\right)tg(2π​−α)

cos⁡ π4\cos\ \frac{\pi}{4}cos 4π​

arctg⁡3ar\operatorname{ctg}\sqrt{3}arctg3​

Найдите arcsin⁡(−π2)\arcsin\left(-\frac{\pi}{2}\right)arcsin(−2π​)

Существует ли такой угол, для которого sin⁡α=−3\sin\alpha=-\sqrt{3}sinα=−3​

arcsin(1) =

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$\sin2x=$

$\cos\left(\frac{3\pi}{2}-\alpha\right)$

$\cos\left(\frac{3\pi}{2}-\alpha\right)$

$tg\left(\frac{\pi}{2}-\alpha\right)$

$\cos\ \frac{\pi}{4}$

$ar\operatorname{ctg}\sqrt{3}$

Найдите $\arcsin\left(-\frac{\pi}{2}\right)$

Существует ли такой угол, для которого $\sin\alpha=-\sqrt{3}$