Solve equation for 0 ≤ θ < 2 π 0\le\theta<2\pi 0 ≤ θ < 2 π . − 2 + cot ⁡ θ = − 3 -2+\cot\theta=-3 − 2 + cot θ = − 3

θ = 3 π 4 , 7 π 4 \theta=\frac{3\pi}{4},\frac{7\pi}{4} θ = 4 3 π , 4 7 π

θ = 3 π 4 , 4 π 3 , 7 π 4 \theta=\frac{3\pi}{4},\frac{4\pi}{3},\frac{7\pi}{4} θ = 4 3 π , 3 4 π , 4 7 π

θ = π 3 , 4 π 3 \theta=\frac{\pi}{3},\frac{4\pi}{3} θ = 3 π , 3 4 π

θ = 3 π 4 , 4 π 3 \theta=\frac{3\pi}{4},\frac{4\pi}{3} θ = 4 3 π , 3 4 π

Solve equation for 0 ≤ θ < 2 π 0\le\theta<2\pi 0 ≤ θ < 2 π . 2 = − 4 − 3 csc ⁡ θ 2=-4-3\csc\theta 2 = − 4 − 3 csc θ

θ = 7 π 6 , 11 π 6 \theta=\frac{7\pi}{6},\frac{11\pi}{6} θ = 6 7 π , 6 1 1 π

θ = 2 π 3 , 7 π 6 \theta=\frac{2\pi}{3},\frac{7\pi}{6} θ = 3 2 π , 6 7 π

θ = π 3 \theta=\frac{\pi}{3} θ = 3 π

θ = 2 π 3 , 7 π 6 , 11 π 6 \theta=\frac{2\pi}{3},\frac{7\pi}{6},\frac{11\pi}{6} θ = 3 2 π , 6 7 π , 6 1 1 π

Solve equation for 0 ≤ θ < 2 π 0\le\theta<2\pi 0 ≤ θ < 2 π . 6 tan ⁡ θ + 6 3 = 0 6\tan\theta\ +\ 6\sqrt{3}\ =\ 0 6 tan θ + 6 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"> = 0

θ = 2 π 3 , 5 π 3 \theta=\frac{2\pi}{3},\frac{5\pi}{3} θ = 3 2 π , 3 5 π

θ = π 6 , 7 π 6 \theta=\frac{\pi}{6},\frac{7\pi}{6} θ = 6 π , 6 7 π

θ = 5 π 6 , 11 π 6 \theta=\frac{5\pi}{6},\frac{11\pi}{6} θ = 6 5 π , 6 1 1 π

θ = π 3 , 4 π 3 \theta=\frac{\pi}{3},\frac{4\pi}{3} θ = 3 π , 3 4 π

S o l v e cos ⁡ x tan ⁡ x + cos ⁡ x = 0 f o r 0 ≤ x < 2 π Solve\ \ \cos x\ \tan x\ +\ \cos x\ =\ 0\ \ for\ 0\ \le\ x\ <\ 2\pi S o l v e cos x tan x + cos x = 0 f o r 0 ≤ x < 2 π

π 2 , 3 π 4 , 3 π 2 , 7 π 4 \frac{\pi}{2},\ \frac{3\pi}{4},\ \frac{3\pi}{2},\ \frac{7\pi}{4} 2 π , 4 3 π , 2 3 π , 4 7 π

π 4 , π 2 , 5 π 4 , 3 π 2 \frac{\pi}{4},\ \frac{\pi}{2},\ \frac{5\pi}{4},\ \frac{3\pi}{2} 4 π , 2 π , 4 5 π , 2 3 π

0 , 3 π 4 , π , 7 π 4 0,\ \frac{3\pi}{4},\ \pi,\ \frac{7\pi}{4} 0 , 4 3 π , π , 4 7 π

0 , π 4 , π , 5 π 4 0,\ \frac{\pi}{4},\ \pi,\ \frac{5\pi}{4} 0 , 4 π , π , 4 5 π

Solve the equation. Restrict your answer to [0,2π). − 2 2 = 4 sin ⁡ 3 θ -2\sqrt{2}=4\sin3\theta − 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"> = 4 sin 3 θ

{ 5 π 12 , 7 π 12 , 13 π 12 , 5 π 4 , 7 π 4 , 23 π 12 } \left\{\frac{5\pi}{12},\frac{7\pi}{12},\frac{13\pi}{12},\frac{5\pi}{4},\frac{7\pi}{4},\frac{23\pi}{12}\right\} { 1 2 5 π , 1 2 7 π , 1 2 1 3 π , 4 5 π , 4 7 π , 1 2 2 3 π }

{ π 24 , 13 π 24 , 7 π 12 , 25 π 24 , 29 π 24 , 5 π 4 , 7 π 4 } \left\{\frac{\pi}{24},\frac{13\pi}{24},\frac{7\pi}{12},\frac{25\pi}{24},\frac{29\pi}{24},\frac{5\pi}{4},\frac{7\pi}{4}\right\} { 2 4 π , 2 4 1 3 π , 1 2 7 π , 2 4 2 5 π , 2 4 2 9 π , 4 5 π , 4 7 π }

{ 7 π 12 , 25 π 24 , 13 π 12 , 7 π 4 , 23 π 12 } \left\{\frac{7\pi}{12},\frac{25\pi}{24},\frac{13\pi}{12},\frac{7\pi}{4},\frac{23\pi}{12}\right\} { 1 2 7 π , 2 4 2 5 π , 1 2 1 3 π , 4 7 π , 1 2 2 3 π }

{ 25 π 24 , 41 π 24 , 7 π 4 } \left\{\frac{25\pi}{24},\frac{41\pi}{24},\frac{7\pi}{4}\right\} { 2 4 2 5 π , 2 4 4 1 π , 4 7 π }

State the solutions in the interval [ 0 , 2 π ) \left[0,\ 2\pi\right) [ 0 , 2 π ) 3 tan ⁡ 3 x − 3 = 0 3\tan3x\ -\ \sqrt{3}\ =\ 0 3 tan 3 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"> = 0

π 18 , 7 π 18 , 13 π 18 , 19 π 18 , 25 π 18 , 31 π 18 \frac{\pi}{18},\ \frac{7\pi}{18},\ \frac{13\pi}{18},\ \frac{19\pi}{18},\ \frac{25\pi}{18},\ \frac{31\pi}{18} 1 8 π , 1 8 7 π , 1 8 1 3 π , 1 8 1 9 π , 1 8 2 5 π , 1 8 3 1 π

π 18 , 13 π 18 , 25 π 18 \frac{\pi}{18},\ \frac{13\pi}{18},\ \frac{25\pi}{18} 1 8 π , 1 8 1 3 π , 1 8 2 5 π

7 π 18 , 19 π 18 , 31 π 18 \frac{7\pi}{18},\ \frac{19\pi}{18},\ \frac{31\pi}{18} 1 8 7 π , 1 8 1 9 π , 1 8 3 1 π

π 9 , 4 π 9 , 7 π 9 , 10 π 9 , 13 π 9 , 16 π 9 \frac{\pi}{9},\ \frac{4\pi}{9},\ \frac{7\pi}{9},\ \frac{10\pi}{9},\ \frac{13\pi}{9},\ \frac{16\pi}{9} 9 π , 9 4 π , 9 7 π , 9 1 0 π , 9 1 3 π , 9 1 6 π

Solving Trig Equations

Authored by Jennifer Wagner

Mathematics

9th - 12th Grade

CCSS covered

Used 259+ times

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15 questions

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve: 4sinθ + 1 = 3
State all solutions in the interval [0, 2π)

π/ 6, 7π/6

π/6, 5π/ 6

5π/6, 7π/6

7π/6, 11π/6

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve: 2cscθ + 2 = 0
State all solutions in the interval [0, 2π)

π/2, 3π/2

π/2

3π /2

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve: $2\sqrt{3}\sec\theta\ +\ 4\ =\ 0$
State all solutions in the interval [0, 2π)

π /3, 2π/3

2π /3, 4π/3

π /6, 5π/6

5π /6, 7π/6

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve: 2cosx - 4 = 0
State all solutions in the interval [0, 2π)

No solution

π/3, 5π/3

π/6, 11π/6

2π/3, 4π/3

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve: 4sin²x = 3
State all solutions in the interval [0, 2π)

π/6, 11π/6

π/3, 2π/3

π/6, 5π/6, 7π/6, 11π/6

π/3, 2π/3, 4π/3, 5π/3

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve equation for $0\le\theta<2\pi$ .
$-2+\cot\theta=-3$

$\theta=\frac{3\pi}{4},\frac{4\pi}{3},\frac{7\pi}{4}$

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

$\theta=\frac{3\pi}{4},\frac{4\pi}{3}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve equation for $0\le\theta<2\pi$ .
$2=-4-3\csc\theta$

$\theta=\frac{2\pi}{3},\frac{7\pi}{6}$

$\theta=\frac{\pi}{3}$

$\theta=\frac{7\pi}{6},\frac{11\pi}{6}$

$\theta=\frac{2\pi}{3},\frac{7\pi}{6},\frac{11\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve equation for $0\le\theta<2\pi$ .
$-1-2\sec^2\theta=-3\sec^2\theta$

$\theta=0,\pi,\frac{4\pi}{3}$

$\theta=0$

$\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

$\theta=0,\pi$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve equation for $0\le\theta<2\pi$ .
$3\tan^2\theta\ -1\ =\ 0$

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$

$\theta=\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$

$\theta=\frac{\pi}{6},\frac{7\pi}{6}$

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

Tags

CCSS.HSF.TF.B.7

10.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve equation for $0\le\theta<2\pi$ .
$6\tan\theta\ +\ 6\sqrt{3}\ =\ 0$

$\theta=\frac{\pi}{6},\frac{7\pi}{6}$

$\theta=\frac{5\pi}{6},\frac{11\pi}{6}$

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

$\theta=\frac{2\pi}{3},\frac{5\pi}{3}$

Tags

CCSS.HSF.TF.B.7

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Solving Trig Equations

Solve: 4sinθ + 1 = 3State all solutions in the interval [0, 2π)

Solve: 2cscθ + 2 = 0State all solutions in the interval [0, 2π)

Solve: 23sec⁡θ + 4 = 02\sqrt{3}\sec\theta\ +\ 4\ =\ 023​secθ + 4 = 0 State all solutions in the interval [0, 2π)

Solve: 2cosx - 4 = 0State all solutions in the interval [0, 2π)

Solve: 4sin2x = 3State all solutions in the interval [0, 2π)

Solve equation for 0≤θ<2π0\le\theta<2\pi0≤θ<2π . −2+cot⁡θ=−3-2+\cot\theta=-3−2+cotθ=−3

Solve equation for 0≤θ<2π0\le\theta<2\pi0≤θ<2π . 2=−4−3csc⁡θ2=-4-3\csc\theta2=−4−3cscθ

Solve equation for 0≤θ<2π0\le\theta<2\pi0≤θ<2π . −1−2sec⁡2θ=−3sec⁡2θ-1-2\sec^2\theta=-3\sec^2\theta−1−2sec2θ=−3sec2θ

Solve equation for 0≤θ<2π0\le\theta<2\pi0≤θ<2π . 3tan⁡2θ −1 = 03\tan^2\theta\ -1\ =\ 03tan2θ −1 = 0

Solve equation for 0≤θ<2π0\le\theta<2\pi0≤θ<2π . 6tan⁡θ + 63 = 06\tan\theta\ +\ 6\sqrt{3}\ =\ 06tanθ + 63​ = 0

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Solve: 4sinθ + 1 = 3
State all solutions in the interval [0, 2π)

Solve: 2cscθ + 2 = 0
State all solutions in the interval [0, 2π)

Solve: $2\sqrt{3}\sec\theta\ +\ 4\ =\ 0$
State all solutions in the interval [0, 2π)

Solve: 2cosx - 4 = 0
State all solutions in the interval [0, 2π)

Solve: 4sin²x = 3
State all solutions in the interval [0, 2π)

Solve equation for $0\le\theta<2\pi$ .
$-2+\cot\theta=-3$

Solve equation for $0\le\theta<2\pi$ .
$2=-4-3\csc\theta$

Solve equation for $0\le\theta<2\pi$ .
$-1-2\sec^2\theta=-3\sec^2\theta$

Solve equation for $0\le\theta<2\pi$ .
$3\tan^2\theta\ -1\ =\ 0$

Solve equation for $0\le\theta<2\pi$ .
$6\tan\theta\ +\ 6\sqrt{3}\ =\ 0$