Teisendage kraadid radiaanideks. 225 ° 225\degree 2 2 5 °

5 π 4 \frac{5\pi}{4} 4 5 π rad

4 π 5 \frac{4\pi}{5} 5 4 π rad

Teisendage radiaanid kraadideks. 7 π 10 \frac{7\pi}{10} 1 0 7 π rad

12 , 6 ° 12,6\degree 1 2 , 6 °

Leidke täpne väärtus. sin ⁡ ( − π 6 ) = . . . \sin\ \left(-\frac{\pi}{6}\right)=... sin ( − 6 π ) = . . .

. . . = − sin ⁡ π 6 = − 1 2 ...=-\sin\frac{\pi}{6}=-\frac{1}{2} . . . = − sin 6 π = − 2 1

. . . = − sin ⁡ 60 ° = − 3 2 ...=-\sin60\degree=-\frac{\sqrt{3}}{2} . . . = − sin 6 0 ° = − 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 ⁡ π 6 = 1 2 ...=\sin\frac{\pi}{6}=\frac{1}{2} . . . = sin 6 π = 2 1

Leidke täpne väärtus. cos ⁡ ( − 45 ° ) = . . . \cos\ \left(-45\degree\right)=... cos ( − 4 5 ° ) = . . .

. . . = cos ⁡ 45 ° = 2 2 ...=\cos45\degree=\frac{\sqrt{2}}{2} . . . = cos 4 5 ° = 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 ⁡ 45 ° = 3 3 ...=\cos45\degree=\frac{\sqrt{3}}{3} . . . = cos 4 5 ° = 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">

. . . = − cos ⁡ 45 ° = − 2 2 ...=-\cos45\degree=-\frac{\sqrt{2}}{2} . . . = − cos 4 5 ° = − 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 ⁡ 45 ° = − 2 3 ...=-\cos45\degree=-\frac{\sqrt{2}}{3} . . . = − cos 4 5 ° = − 3 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">

Leidke cos ⁡ α \cos\alpha cos α , kui sin ⁡ α = 40 41 \sin\alpha=\frac{40}{41} sin α = 4 1 4 0 ja α \alpha α on II veerandi nurk.

− 9 41 -\frac{9}{41} − 4 1 9

102 ° 4 1 ′ 102\degree41' 1 0 2 ° 4 1 ′

Leike cot ⁡ α \cot\alpha cot α , kui tan ⁡ α = − 33 56 \tan\alpha=-\frac{33}{56} tan α = − 5 6 3 3 ja α \alpha α on III veerandi nurk.

cot ⁡ α = 56 33 \cot\alpha=\frac{56}{33} cot α = 3 3 5 6

− 30 ° 3 1 ′ -30\degree31' − 3 0 ° 3 1 ′

cot ⁡ α = − 56 33 \cot\alpha=-\frac{56}{33} cot α = − 3 3 5 6

Lihtsustage avaldis. sin ⁡ ( π + α ) − sin ⁡ ( π − α ) = . . . \sin\left(\pi+\alpha\right)-\sin\left(\pi-\alpha\right)=... sin ( π + α ) − sin ( π − α ) = . . .

. . . = − sin ⁡ α − sin ⁡ α = − 2 sin ⁡ α ...=-\sin\alpha-\sin\alpha=-2\sin\alpha . . . = − sin α − sin α = − 2 sin α

. . . = − sin ⁡ α + sin ⁡ α = 0 ...=-\sin\alpha+\sin\alpha=0 . . . = − sin α + sin α = 0

. . . = − cos ⁡ α + cos ⁡ α = 0 ...=-\cos\alpha+\cos\alpha=0 . . . = − cos α + cos α = 0

. . . = − sin ⁡ − sin ⁡ = − 2 sin ⁡ ...=-\sin-\sin=-2\sin . . . = − sin − sin = − 2 sin

Lihtsustage avaldis. cos ⁡ ( 90 ° − α ) − sin ⁡ ( − α ) = . . . \cos\left(90\degree-\alpha\right)-\sin\left(-\alpha\right)=... cos ( 9 0 ° − α ) − sin ( − α ) = . . .

. . . = sin ⁡ α + sin ⁡ α = 2 sin ⁡ α ...=\sin\alpha+\sin\alpha=2\sin\alpha . . . = sin α + sin α = 2 sin α

. . . = sin ⁡ α − sin ⁡ α = 0 ...=\sin\alpha-\sin\alpha=0 . . . = sin α − sin α = 0

. . . = cos ⁡ α + sin ⁡ α ...=\cos\alpha+\sin\alpha . . . = cos α + sin α

. . . = cos ⁡ α + cos ⁡ α = 2 cos ⁡ α ...=\cos\alpha+\cos\alpha=2\cos\alpha . . . = cos α + cos α = 2 cos α

Esita nurk 2350 ° 2350\degree 2 3 5 0 ° kujul α + n ⋅ 360 ° \alpha+n\cdot360\degree α + n ⋅ 3 6 0 ° , kus n ∈ Z n\in Z n ∈ Z ja 0 ° ≤ α < 360 ° . 0\degree\le\alpha<360\degree. 0 ° ≤ α < 3 6 0 ° .

2350 ° = 190 ° + 6 ⋅ 360 ° 2350\degree=190\degree+6\cdot360\degree 2 3 5 0 ° = 1 9 0 ° + 6 ⋅ 3 6 0 °

2350 ° = 550 ° + 5 ⋅ 360 ° 2350\degree=550\degree+5\cdot360\degree 2 3 5 0 ° = 5 5 0 ° + 5 ⋅ 3 6 0 °

2350 ° = 180 ° + 6 ⋅ 360 ° 2350\degree=180\degree+6\cdot360\degree 2 3 5 0 ° = 1 8 0 ° + 6 ⋅ 3 6 0 °

2350 ° = 190 ° − 6 ⋅ 360 ° 2350\degree=190\degree-6\cdot360\degree 2 3 5 0 ° = 1 9 0 ° − 6 ⋅ 3 6 0 °

Esita nurk − 4060 ° -4060\degree − 4 0 6 0 ° kujul α + n ⋅ 360 ° \alpha+n\cdot360\degree α + n ⋅ 3 6 0 ° , kus n ∈ Z n\in Z n ∈ Z ja 0 ° ≤ α < 360 ° 0\degree\le\alpha<360\degree 0 ° ≤ α < 3 6 0 ° .

− 4060 ° = 260 ° − 12 ⋅ 360 ° -4060\degree=260\degree-12\cdot360\degree − 4 0 6 0 ° = 2 6 0 ° − 1 2 ⋅ 3 6 0 °

− 4060 ° = 260 ° + 12 ⋅ 360 ° -4060\degree=260\degree+12\cdot360\degree − 4 0 6 0 ° = 2 6 0 ° + 1 2 ⋅ 3 6 0 °

− 4060 ° = 260 ° − 13 ⋅ 360 ° -4060\degree=260\degree-13\cdot360\degree − 4 0 6 0 ° = 2 6 0 ° − 1 3 ⋅ 3 6 0 °

− 4060 ° = − 100 ° − 11 ⋅ 360 ° -4060\degree=-100\degree-11\cdot360\degree − 4 0 6 0 ° = − 1 0 0 ° − 1 1 ⋅ 3 6 0 °

Leidke sin ⁡ α \sin\alpha sin α , kui cos ⁡ α = − 2 3 \cos\alpha=-\frac{\sqrt{2}}{3} cos α = − 3 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"> ja π < α < 3 π 2 \pi<\alpha<\frac{3\pi}{2} π < α < 2 3 π .

− 7 3 -\frac{\sqrt{7}}{3} − 3 7 <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">

7 3 \frac{\sqrt{7}}{3} 3 7 <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 ⁡ α ≈ 0 , 882 \sin\alpha\approx0,882 sin α ≈ 0 , 8 8 2

sin ⁡ α ≈ − 0 , 881 \sin\alpha\approx-0,881 sin α ≈ − 0 , 8 8 1

Väljendage täiendusnurga kaudu. cos ⁡ ( π 2 + α ) \cos\left(\frac{\pi}{2}+\alpha\right) cos ( 2 π + α )

sin ⁡ ( − α ) \sin\left(-\alpha\right) sin ( − α )

cos ⁡ ( − α ) \cos\left(-\alpha\right) cos ( − α )

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

Lihtsusta avaldis cos ⁡ ( − 288 ° ) tan ⁡ 72 ° \cos\left(-288\degree\right)\tan72\degree cos ( − 2 8 8 ° ) tan 7 2 °

sin ⁡ 72 ° \sin72\degree sin 7 2 °

cos ⁡ 72 ° \cos72\degree cos 7 2 °

− sin ⁡ 72 ° -\sin72\degree − sin 7 2 °

− cos ⁡ 72 ° -\cos72\degree − cos 7 2 °

Trigonomeetria taandamisvalemid (10. klass)

Authored by Auli Reitel

Mathematics

10th - 12th Grade

Used 15+ times

Trigonomeetria taandamisvalemid (10. klass)

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

Teisendage kraadid radiaanideks.

$225\degree$

$225\pi\$ rad

$\frac{5\pi}{4}$ rad

$\frac{5}{4}$ rad

$\frac{4\pi}{5}$ rad

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Teisendage radiaanid kraadideks.
$\frac{7\pi}{10}$ rad

$170\degree$

$127\degree$

$12,6\degree$

$126\degree$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Teisendage radiaanid kraadideks. Lõppvastus esita nurgaminuti täpsusega.
$3,2$ rad

$183\degree20'$

$183\degree21'$

$183\degree20'47''$

$183\degree$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Leidke täpne väärtus.

$\sin\ \left(-\frac{\pi}{6}\right)=...$

$...=$ väärtus puudub

$...=-\sin60\degree=-\frac{\sqrt{3}}{2}$

$...=\sin\frac{\pi}{6}=\frac{1}{2}$

$...=-\sin\frac{\pi}{6}=-\frac{1}{2}$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Leidke täpne väärtus.
$\cos\ \left(-45\degree\right)=...$

$...=\cos45\degree=\frac{\sqrt{3}}{3}$

$...=-\cos45\degree=-\frac{\sqrt{2}}{2}$

$...=\cos45\degree=\frac{\sqrt{2}}{2}$

$...=-\cos45\degree=-\frac{\sqrt{2}}{3}$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Avaldage nurk I veerandi nurgana ja leidke funktsiooni täpne väärtus.

$\cos\ 150\degree=...$

$...=-\cos\ 60\degree=-\frac{1}{2}$

$...=-\cos\ 30\degree=-\frac{\sqrt{3}}{2}$

$...=\cos\ 30\degree=\frac{\sqrt{3}}{2}$

$...=-\cos\ 30\degree=-\frac{1}{2}$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Avaldage nurk I veerandi nurgana ja leidke funktsiooni täpne väärtus.
$\tan\ 585\degree=...$

$\tan\ \left(180\degree+45\degree\right)=\tan45\degree=1$

$\tan\ \left(180\degree+45\degree\right)=-\tan45\degree=-1$

$\tan\ \left(180\degree+45\degree\right)=\tan45\degree=\frac{\sqrt{2}}{2}$

$\tan\ \left(360\degree-135\degree\right)=-\tan135\degree=-1$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Leidke $\cos\alpha$ , kui $\sin\alpha=\frac{40}{41}$ ja $\alpha$ on II veerandi nurk.

Seda ei saa leida, sest andmed on vastuolulised.

$-\frac{9}{41}$

$\frac{9}{41}$

$102\degree41'$

$-0,21$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Leike $\cot\alpha$ , kui $\tan\alpha=-\frac{33}{56}$ ja $\alpha$ on III veerandi nurk.

$\cot\alpha=\frac{56}{33}$

$-30\degree31'$

$\cot\alpha=-\frac{56}{33}$

Seda ei saa leida, andmed on vastuolulised.

10.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Lihtsustage avaldis.

$\sin\left(\pi+\alpha\right)-\sin\left(\pi-\alpha\right)=...$

$...=-\sin\alpha+\sin\alpha=0$

$...=-\sin\alpha-\sin\alpha=-2\sin\alpha$

$...=-\cos\alpha+\cos\alpha=0$

$...=-\sin-\sin=-2\sin$

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Trigonomeetria taandamisvalemid (10. klass)

Teisendage kraadid radiaanideks. 225°225\degree225°

Teisendage radiaanid kraadideks. 7π10\frac{7\pi}{10}107π​ rad

Teisendage radiaanid kraadideks. Lõppvastus esita nurgaminuti täpsusega. 3,23,23,2 rad

Leidke täpne väärtus. sin⁡ (−π6)=...\sin\ \left(-\frac{\pi}{6}\right)=...sin (−6π​)=...

Leidke täpne väärtus. cos⁡ (−45°)=...\cos\ \left(-45\degree\right)=...cos (−45°)=...

Avaldage nurk I veerandi nurgana ja leidke funktsiooni täpne väärtus. cos⁡ 150°=...\cos\ 150\degree=...cos 150°=...

Avaldage nurk I veerandi nurgana ja leidke funktsiooni täpne väärtus. tan⁡ 585°=...\tan\ 585\degree=...tan 585°=...

Leidke cos⁡α\cos\alphacosα , kui sin⁡α=4041\sin\alpha=\frac{40}{41}sinα=4140​ ja α\alphaα on II veerandi nurk.

Leike cot⁡α\cot\alphacotα , kui tan⁡α=−3356\tan\alpha=-\frac{33}{56}tanα=−5633​ ja α\alphaα on III veerandi nurk.

Lihtsustage avaldis. sin⁡(π+α)−sin⁡(π−α)=...\sin\left(\pi+\alpha\right)-\sin\left(\pi-\alpha\right)=...sin(π+α)−sin(π−α)=...

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Teisendage kraadid radiaanideks.

$225\degree$

Teisendage radiaanid kraadideks.
$\frac{7\pi}{10}$ rad

Teisendage radiaanid kraadideks. Lõppvastus esita nurgaminuti täpsusega.
$3,2$ rad

Leidke täpne väärtus.

$\sin\ \left(-\frac{\pi}{6}\right)=...$

Leidke täpne väärtus.
$\cos\ \left(-45\degree\right)=...$

Avaldage nurk I veerandi nurgana ja leidke funktsiooni täpne väärtus.

$\cos\ 150\degree=...$

Avaldage nurk I veerandi nurgana ja leidke funktsiooni täpne väärtus.
$\tan\ 585\degree=...$

Leidke $\cos\alpha$ , kui $\sin\alpha=\frac{40}{41}$ ja $\alpha$ on II veerandi nurk.

Leike $\cot\alpha$ , kui $\tan\alpha=-\frac{33}{56}$ ja $\alpha$ on III veerandi nurk.

Lihtsustage avaldis.

$\sin\left(\pi+\alpha\right)-\sin\left(\pi-\alpha\right)=...$