Nilai x dalam selang 0 o ≤ x ≤ 36 0 o 0^o\le x\le360^o 0 o ≤ x ≤ 3 6 0 o yang memenuhi persamaan cos ⁡ x = 1 2 2 \cos\ x=\frac{1}{2}\sqrt{2} cos x = 2 1 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"> adalah . . .

4 5 o 45^o 4 5 o dan 31 5 o 315^o 3 1 5 o

6 0 o 60^o 6 0 o dan 30 0 o 300^o 3 0 0 o

3 0 o 30^o 3 0 o dan 35 0 o 350^o 3 5 0 o

9 0 o 90^o 9 0 o dan 27 0 o 270^o 2 7 0 o

18 0 o 180^o 1 8 0 o dan 18 0 o 180^o 1 8 0 o

Himpunan penyelesaian dari persamaan trigonometri \cos\ x=-\frac{1}{2} cos x = − 2 1 untuk 0 ≤ x ≤ 2 π 0\le x\le2\pi 0 ≤ x ≤ 2 π adalah . . .

{ 2 3 π , 4 3 π } \left\{\frac{2}{3}\pi,\ \frac{4}{3}\pi\right\} { 3 2 π , 3 4 π }

{ 1 3 π } \left\{\frac{1}{3}\pi\right\} { 3 1 π }

{ 1 6 π } \left\{\frac{1}{6}\pi\right\} { 6 1 π }

{ 2 3 π } \left\{\frac{2}{3}\pi\right\} { 3 2 π }

{ 4 3 π } \left\{\frac{4}{3}\pi\right\} { 3 4 π }

Diketahui persamaan \sqrt{2}.\cos\ x-1=0 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 x − 1 = 0 untuk 0 o ≤ x ≤ 36 0 o 0^o\le x\le360^o 0 o ≤ x ≤ 3 6 0 o . Himpunan penyelesaian persamaan tersebut adalah . . .

{ 4 5 o , 31 5 o } \left\{45^o,\ 315^o\right\} { 4 5 o , 3 1 5 o }

{ 4 5 o , 13 5 o } \left\{45^o,\ 135^o\right\} { 4 5 o , 1 3 5 o }

{ 4 5 o , 22 5 o } \left\{45^o,\ 225^o\right\} { 4 5 o , 2 2 5 o }

{ 4 5 o } \left\{45^o\right\} { 4 5 o }

{ 4 5 o , 13 5 o , 22 5 o , 31 5 o } \left\{45^o,\ 135^o,\ 225^o,\ 315^o\right\} { 4 5 o , 1 3 5 o , 2 2 5 o , 3 1 5 o }

Himpunan penyelesaian dari persamaan 2\ .\sin\ x\ -\sqrt{2}=0 2 . sin x − 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"> = 0 adalah . . .

{ 4 5 o , 13 5 o } \left\{45^o,\ 135^o\right\} { 4 5 o , 1 3 5 o }

{ 4 5 o } \left\{45^o\right\} { 4 5 o }

{ 13 5 o } \left\{135^o\right\} { 1 3 5 o }

{ 4 5 o , 13 5 o , 24 0 o } \left\{45^o,\ 135^o,\ 240^o\right\} { 4 5 o , 1 3 5 o , 2 4 0 o }

{ 4 5 o , 13 5 o , 18 5 o , 24 0 o } \left\{45^o,\ 135^o,\ 185^o,\ 240^o\right\} { 4 5 o , 1 3 5 o , 1 8 5 o , 2 4 0 o }

Himpunan penyelesaian dari persamaan 1+2\ .\ \cos\ 2x=0 1 + 2 . cos 2 x = 0 untuk 0 o ≤ x ≤ 36 0 o 0^o\le x\le360^o 0 o ≤ x ≤ 3 6 0 o adalah . . .

{ 6 0 o , 12 0 o , 24 0 o , 30 0 o } \left\{60^o,\ 120^o,\ 240^o,\ 300^o\right\} { 6 0 o , 1 2 0 o , 2 4 0 o , 3 0 0 o }

{ 12 0 o } \left\{120^o\right\} { 1 2 0 o }

{ 30 0 o } \left\{300^o\right\} { 3 0 0 o }

{ 12 0 o , 30 0 o } \left\{120^o,\ 300^o\right\} { 1 2 0 o , 3 0 0 o }

{ 12 0 o , 24 0 o , 30 0 o } \left\{120^o,\ 240^o,\ 300^o\right\} { 1 2 0 o , 2 4 0 o , 3 0 0 o }

Jika α \alpha α , β \beta β , dan γ \gamma γ adalah sudut-sudut sebuah segitiga maka sin ⁡ 1 2 ( β + γ ) \sin\ \frac{1}{2}\left(\beta+\gamma\right) sin 2 1 ( β + γ ) adalah . . .

cos ⁡ ( 1 2 α ) \cos\left(\frac{1}{2}\alpha\right) cos ( 2 1 α )

sin ⁡ ( 1 2 α ) \sin\left(\frac{1}{2}\alpha\right) sin ( 2 1 α )

sin ⁡ ( 1 2 β ) \sin\left(\frac{1}{2}\beta\right) sin ( 2 1 β )

cos ⁡ ( 1 2 β ) \cos\left(\frac{1}{2}\beta\right) cos ( 2 1 β )

− cos ⁡ ( 1 2 β ) -\cos\left(\frac{1}{2}\beta\right) − cos ( 2 1 β )

Jika tan ⁡ x = 2 \tan x=2 tan x = 2 dan sin ⁡ ( x − y ) = 5 ⋅ cos ⁡ ( y − x ) \sin\left(x-y\right)=5\cdot\cos\left(y-x\right) sin ( x − y ) = 5 ⋅ cos ( y − x ) maka tan ⁡ y = \tan y= tan y = . . .

− 3 11 -\frac{3}{11} − 1 1 3

Diketahui Δ A B C \Delta ABC Δ A B C , dengan sin ⁡ A = 0 , 6 \sin A=0,6 sin A = 0 , 6 dan tan ⁡ B = 0 , 5 \tan B=0,5 tan B = 0 , 5 . Nilai cos ⁡ ( A − B ) − cos ⁡ C = \cos\left(A-B\right)-\cos C= cos ( A − B ) − cos C = . . .

16 25 5 \frac{16}{25}\sqrt{5} 2 5 1 6 5 <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 5 5 \frac{1}{5}\sqrt{5} 5 1 5 <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 5 5 \frac{2}{5}\sqrt{5} 5 2 5 <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">

4 25 5 \frac{4}{25}\sqrt{5} 2 5 4 5 <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">

8 25 5 \frac{8}{25}\sqrt{5} 2 5 8 5 <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">

Persamaan Trigonometri 1

Authored by Ahmadi Susilo

Mathematics

Professional Development

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15 questions

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Nilai x yang memenuhi persamaan $\tan x=\tan50^o$ adalah . . .

$150^o$

$180^o$

$210^o$

$230^o$

$250^o$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Nilai x yang memenuhi persamaan $\sin\ x\ =\ \sin\ \frac{\pi}{5}$ adalah . . .

$\frac{2\pi}{5}$

$\frac{3\pi}{5}$

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

$\frac{\pi}{2}$

$\frac{2\pi}{3}$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Nilai x yang memenuhi persamaan $\tan\ x=\tan\ \frac{2\pi}{5}$ adalah . . .

$\frac{8\pi}{5}$

$\frac{6\pi}{5}$

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

$\frac{3\pi}{5}$

$\frac{2\pi}{5}$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Nilai x dalam selang $0^o\le x\le360^o$ yang memenuhi persamaan $\cos\ x=\frac{1}{2}\sqrt{2}$ adalah . . .

$45^o$ dan $315^o$

$60^o$ dan $300^o$

$30^o$ dan $350^o$

$90^o$ dan $270^o$

$180^o$ dan $180^o$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Himpunan penyelesaian dari persamaan trigonometri $\cos\ x=-\frac{1}{2}$ untuk $0\le x\le2\pi$ adalah . . .

$\left\{\frac{1}{3}\pi\right\}$

$\left\{\frac{1}{6}\pi\right\}$

$\left\{\frac{2}{3}\pi\right\}$

$\left\{\frac{2}{3}\pi,\ \frac{4}{3}\pi\right\}$

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

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Diketahui persamaan $\sqrt{2}.\cos\ x-1=0$ untuk $0^o\le x\le360^o$ . Himpunan penyelesaian persamaan tersebut adalah . . .

$\left\{45^o,\ 135^o\right\}$

$\left\{45^o,\ 225^o\right\}$

$\left\{45^o,\ 315^o\right\}$

$\left\{45^o\right\}$

$\left\{45^o,\ 135^o,\ 225^o,\ 315^o\right\}$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Himpunan penyelesaian dari persamaan $2\ .\sin\ x\ -\sqrt{2}=0$ adalah . . .

$\left\{45^o\right\}$

$\left\{135^o\right\}$

$\left\{45^o,\ 135^o\right\}$

$\left\{45^o,\ 135^o,\ 240^o\right\}$

$\left\{45^o,\ 135^o,\ 185^o,\ 240^o\right\}$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Himpunan penyelesaian dari persamaan $1+2\ .\ \cos\ 2x=0$ untuk $0^o\le x\le360^o$ adalah . . .

$\left\{120^o\right\}$

$\left\{300^o\right\}$

$\left\{120^o,\ 300^o\right\}$

$\left\{120^o,\ 240^o,\ 300^o\right\}$

$\left\{60^o,\ 120^o,\ 240^o,\ 300^o\right\}$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Nilai x yang memenuhi persamaan $\cos\ x\ =\cos\ 110^o$ adalah . . .

$185^o$

$200^o$

$210^o$

$250^o$

$310^o$

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Nilai x yang memenuhi persamaan $\cos\ x=\cos\ \frac{8\pi}{7}$ adalah . . .

$\frac{3\pi}{7}$

$\frac{4\pi}{7}$

$\frac{5\pi}{7}$

$\frac{6\pi}{7}$

$\pi$

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Persamaan Trigonometri 1

Nilai x yang memenuhi persamaan tan⁡x=tan⁡50o\tan x=\tan50^otanx=tan50o adalah . . .

Nilai x yang memenuhi persamaan sin⁡ x = sin⁡ π5\sin\ x\ =\ \sin\ \frac{\pi}{5}sin x = sin 5π​ adalah . . .

Nilai x yang memenuhi persamaan tan⁡ x=tan⁡ 2π5\tan\ x=\tan\ \frac{2\pi}{5}tan x=tan 52π​ adalah . . .

Nilai x dalam selang 0o≤x≤360o0^o\le x\le360^o0o≤x≤360o yang memenuhi persamaan cos⁡ x=122\cos\ x=\frac{1}{2}\sqrt{2}cos x=21​2​ adalah . . .

Himpunan penyelesaian dari persamaan trigonometri \cos\ x=-\frac{1}{2}cos x=−21​ untuk 0≤x≤2π0\le x\le2\pi0≤x≤2π adalah . . .

Diketahui persamaan \sqrt{2}.\cos\ x-1=02​.cos x−1=0 untuk 0o≤x≤360o0^o\le x\le360^o0o≤x≤360o . Himpunan penyelesaian persamaan tersebut adalah . . .

Himpunan penyelesaian dari persamaan 2\ .\sin\ x\ -\sqrt{2}=02 .sin x −2​=0 adalah . . .

Himpunan penyelesaian dari persamaan 1+2\ .\ \cos\ 2x=01+2 . cos 2x=0 untuk 0o≤x≤360o0^o\le x\le360^o0o≤x≤360o adalah . . .

Nilai x yang memenuhi persamaan \cos\ x\ =\cos\ 110^ocos x =cos 110o adalah . . .

Nilai x yang memenuhi persamaan \cos\ x=\cos\ \frac{8\pi}{7}cos x=cos 78π​ adalah . . .

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Nilai x yang memenuhi persamaan $\tan x=\tan50^o$ adalah . . .

Nilai x yang memenuhi persamaan $\sin\ x\ =\ \sin\ \frac{\pi}{5}$ adalah . . .

Nilai x yang memenuhi persamaan $\tan\ x=\tan\ \frac{2\pi}{5}$ adalah . . .

Nilai x dalam selang $0^o\le x\le360^o$ yang memenuhi persamaan $\cos\ x=\frac{1}{2}\sqrt{2}$ adalah . . .

Himpunan penyelesaian dari persamaan trigonometri $\cos\ x=-\frac{1}{2}$ untuk $0\le x\le2\pi$ adalah . . .

Diketahui persamaan $\sqrt{2}.\cos\ x-1=0$ untuk $0^o\le x\le360^o$ . Himpunan penyelesaian persamaan tersebut adalah . . .

Himpunan penyelesaian dari persamaan $2\ .\sin\ x\ -\sqrt{2}=0$ adalah . . .

Himpunan penyelesaian dari persamaan $1+2\ .\ \cos\ 2x=0$ untuk $0^o\le x\le360^o$ adalah . . .

Nilai x yang memenuhi persamaan $\cos\ x\ =\cos\ 110^o$ adalah . . .

Nilai x yang memenuhi persamaan $\cos\ x=\cos\ \frac{8\pi}{7}$ adalah . . .