Solve for ALL answers such that 0 ≤ x < 2 π 0\le x<2\pi 0 ≤ x < 2 π : 0 = sin ⁡ 2 x 0=\sin2x 0 = sin 2 x

x = 0 , π 2 , π , 3 π 2 x=0,\frac{\pi}{2},\pi,\frac{3\pi}{2} x = 0 , 2 π , π , 2 3 π

N o S o l u t i o n s No\ Solutions N o S o l u t i o n s

x = 0 , π , 2 π , 3 π x=0,\pi,2\pi,3\pi x = 0 , π , 2 π , 3 π

Solve for ALL answers such that 0 ≤ x < 2 π 0\le x<2\pi 0 ≤ x < 2 π : 1 2 = sin ⁡ 3 x \frac{1}{2}=\sin3x 2 1 = sin 3 x

x = π 6 , 5 π 6 x=\frac{\pi}{6},\frac{5\pi}{6} x = 6 π , 6 5 π

Solve for ALL answers such that 0 ≤ x < 2 π 0\le x<2\pi 0 ≤ x < 2 π : cos ⁡ 2 x = 2 2 \cos2x=\frac{\sqrt{2}}{2} cos 2 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 8 , 7 π 8 , 9 π 8 , 15 π 8 x=\frac{\pi}{8},\frac{7\pi}{8},\frac{9\pi}{8},\frac{15\pi}{8} x = 8 π , 8 7 π , 8 9 π , 8 1 5 π

x = π 4 , 7 π 4 , 9 π 4 , 15 π 4 x=\frac{\pi}{4},\frac{7\pi}{4},\frac{9\pi}{4},\frac{15\pi}{4} x = 4 π , 4 7 π , 4 9 π , 4 1 5 π

x = π 4 , 7 π 4 x=\frac{\pi}{4},\frac{7\pi}{4} x = 4 π , 4 7 π

N o S o l u t i o n No\ Solution N o S o l u t i o n

Solve for ALL answers such that 0 ≤ x < 2 π 0\le x<2\pi 0 ≤ x < 2 π : csc ⁡ 3 x = − 2 3 3 \csc3x=-\frac{2\sqrt{3}}{3} csc 3 x = − 3 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 = 4 π 9 , 5 π 9 , 10 π 9 , 11 π 9 x=\frac{4\pi}{9},\frac{5\pi}{9},\frac{10\pi}{9},\frac{11\pi}{9} x = 9 4 π , 9 5 π , 9 1 0 π , 9 1 1 π

N o S o l u t i o n s No\ Solutions N o S o l u t i o n s

Solve for ALL answers such that 0 ≤ x < 2 π 0\le x<2\pi 0 ≤ x < 2 π : − 3 2 = cos ⁡ 3 x -\frac{\sqrt{3}}{2}=\cos3x − 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"> = cos 3 x

N o S o l u t i o n s No\ Solutions N o S o l u t i o n s

x = 5 π 6 , 7 π 6 x=\frac{5\pi}{6},\frac{7\pi}{6} x = 6 5 π , 6 7 π

Solve for ALL answers such that 0 ≤ x < 2 π 0\le x<2\pi 0 ≤ x < 2 π : − 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"> = sin x

x = 4 π 3 , 5 π 3 x=\frac{4\pi}{3},\frac{5\pi}{3} x = 3 4 π , 3 5 π

x = π 3 , 2 π 3 x=\frac{\pi}{3},\frac{2\pi}{3} x = 3 π , 3 2 π

N o S o l u t i o n s No\ Solutions N o S o l u t i o n s

x = π 3 , 5 π 3 x=\frac{\pi}{3},\frac{5\pi}{3} x = 3 π , 3 5 π

Solve for ALL answers such that 0 ≤ x < 2 π 0\le x<2\pi 0 ≤ x < 2 π : 3 2 = cos ⁡ 2 x \frac{\sqrt{3}}{2}=\cos2x 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"> = cos 2 x

x = π 12 , 11 π 12 , 13 π 12 , 23 π 12 x=\frac{\pi}{12},\frac{11\pi}{12},\frac{13\pi}{12},\frac{23\pi}{12} x = 1 2 π , 1 2 1 1 π , 1 2 1 3 π , 1 2 2 3 π

x = π 6 , 11 π 6 , 13 π 6 , 23 π 6 x=\frac{\pi}{6},\frac{11\pi}{6},\frac{13\pi}{6},\frac{23\pi}{6} x = 6 π , 6 1 1 π , 6 1 3 π , 6 2 3 π

N o S o l u t i o n s No\ Solutions N o S o l u t i o n s

x = π 6 , 11 π 6 x=\frac{\pi}{6},\frac{11\pi}{6} x = 6 π , 6 1 1 π

Solve for ALL answers such that 0 ≤ x < 2 π 0\le x<2\pi 0 ≤ x < 2 π : tan ⁡ 3 x = 1 \tan3x=1 tan 3 x = 1

N o S o l u t i o n s No\ Solutions N o S o l u t i o n s

x = π 4 , 5 π 4 x=\frac{\pi}{4},\frac{5\pi}{4} x = 4 π , 4 5 π

Solving Trig Equations with Multiple Angles

Authored by Adam Hosler

Mathematics

11th - 12th Grade

CCSS covered

Used 147+ times

Solving Trig Equations with Multiple Angles

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8 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for ALL answers such that
$0\le x<2\pi$ :

$0=\sin2x$

$x=0,\frac{\pi}{2},\pi,\frac{3\pi}{2}$

$x=0,\pi$

$No\ Solutions$

$x=0,\pi,2\pi,3\pi$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for ALL answers such that
$0\le x<2\pi$ :

$\frac{1}{2}=\sin3x$

$x=\frac{\pi}{18},\frac{5\pi}{18},\frac{13\pi}{18},\frac{17\pi}{18},\frac{25\pi}{18},\frac{29\pi}{18}$

$x=\frac{\pi}{18},\frac{5\pi}{18},\frac{13\pi}{18},\frac{17\pi}{18}$

$x=\frac{\pi}{6},\frac{5\pi}{6},\frac{13\pi}{6},\frac{17\pi}{6},\frac{25\pi}{6},\frac{29\pi}{6}$

$x=\frac{\pi}{6},\frac{5\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for ALL answers such that
$0\le x<2\pi$ :

$\cos2x=\frac{\sqrt{2}}{2}$

$x=\frac{\pi}{8},\frac{7\pi}{8},\frac{9\pi}{8},\frac{15\pi}{8}$

$x=\frac{\pi}{4},\frac{7\pi}{4},\frac{9\pi}{4},\frac{15\pi}{4}$

$x=\frac{\pi}{4},\frac{7\pi}{4}$

$No\ Solution$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for ALL answers such that
$0\le x<2\pi$ :

$\csc3x=-\frac{2\sqrt{3}}{3}$

$x=\frac{4\pi}{9},\frac{5\pi}{9},\frac{10\pi}{9},\frac{11\pi}{9}$

$x=\frac{4\pi}{9},\frac{5\pi}{9},\frac{10\pi}{9},\frac{11\pi}{9},\frac{16\pi}{9},\frac{17\pi}{9}$

$x=\frac{4\pi}{3},\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3},\frac{16\pi}{3},\frac{17\pi}{3}$

$No\ Solutions$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for ALL answers such that
$0\le x<2\pi$ :

$-\frac{\sqrt{3}}{2}=\cos3x$

$x=\frac{5\pi}{18},\frac{7\pi}{18},\frac{17\pi}{18},\frac{19\pi}{18},\frac{29\pi}{18},\frac{31\pi}{18}$

$x=\frac{5\pi}{6},\frac{7\pi}{6},\frac{17\pi}{6},\frac{19\pi}{6},\frac{29\pi}{6},\frac{31\pi}{6}$

$No\ Solutions$

$x=\frac{5\pi}{6},\frac{7\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for ALL answers such that
$0\le x<2\pi$ :

$-\frac{\sqrt{3}}{2}=\sin x$

$x=\frac{4\pi}{3},\frac{5\pi}{3}$

$x=\frac{\pi}{3},\frac{2\pi}{3}$

$No\ Solutions$

$x=\frac{\pi}{3},\frac{5\pi}{3}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for ALL answers such that
$0\le x<2\pi$ :

$\frac{\sqrt{3}}{2}=\cos2x$

$x=\frac{\pi}{12},\frac{11\pi}{12},\frac{13\pi}{12},\frac{23\pi}{12}$

$x=\frac{\pi}{6},\frac{11\pi}{6},\frac{13\pi}{6},\frac{23\pi}{6}$

$No\ Solutions$

$x=\frac{\pi}{6},\frac{11\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for ALL answers such that
$0\le x<2\pi$ :

$\tan3x=1$

$x=\frac{\pi}{12},\frac{5\pi}{12},\frac{3\pi}{4},\frac{13\pi}{12},\frac{17\pi}{12},\frac{7\pi}{4}$

$x=\frac{\pi}{4},\frac{5\pi}{4},\frac{9\pi}{4},\frac{13\pi}{4},\frac{17\pi}{4},\frac{21\pi}{4}$

$No\ Solutions$

$x=\frac{\pi}{4},\frac{5\pi}{4}$

Tags

CCSS.HSF.TF.B.7

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Solving Trig Equations with Multiple Angles

Solve for ALL answers such that 0≤x<2π0\le x<2\pi0≤x<2π : 0=sin⁡2x0=\sin2x0=sin2x

Solve for ALL answers such that 0≤x<2π0\le x<2\pi0≤x<2π : 12=sin⁡3x\frac{1}{2}=\sin3x21​=sin3x

Solve for ALL answers such that 0≤x<2π0\le x<2\pi0≤x<2π : cos⁡2x=22\cos2x=\frac{\sqrt{2}}{2}cos2x=22​​

Solve for ALL answers such that 0≤x<2π0\le x<2\pi0≤x<2π : csc⁡3x=−233\csc3x=-\frac{2\sqrt{3}}{3}csc3x=−323​​

Solve for ALL answers such that 0≤x<2π0\le x<2\pi0≤x<2π : −32=cos⁡3x-\frac{\sqrt{3}}{2}=\cos3x−23​​=cos3x

Solve for ALL answers such that 0≤x<2π0\le x<2\pi0≤x<2π : −32=sin⁡x-\frac{\sqrt{3}}{2}=\sin x−23​​=sinx

Solve for ALL answers such that 0≤x<2π0\le x<2\pi0≤x<2π : 32=cos⁡2x\frac{\sqrt{3}}{2}=\cos2x23​​=cos2x

Solve for ALL answers such that 0≤x<2π0\le x<2\pi0≤x<2π : tan⁡3x=1\tan3x=1tan3x=1

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Solve for ALL answers such that
$0\le x<2\pi$ :

$0=\sin2x$

Solve for ALL answers such that
$0\le x<2\pi$ :

$\frac{1}{2}=\sin3x$

Solve for ALL answers such that
$0\le x<2\pi$ :

$\cos2x=\frac{\sqrt{2}}{2}$

Solve for ALL answers such that
$0\le x<2\pi$ :

$\csc3x=-\frac{2\sqrt{3}}{3}$

Solve for ALL answers such that
$0\le x<2\pi$ :

$-\frac{\sqrt{3}}{2}=\cos3x$

Solve for ALL answers such that
$0\le x<2\pi$ :

$-\frac{\sqrt{3}}{2}=\sin x$

Solve for ALL answers such that
$0\le x<2\pi$ :

$\frac{\sqrt{3}}{2}=\cos2x$

Solve for ALL answers such that
$0\le x<2\pi$ :

$\tan3x=1$