Solve for θ ∈ [ 0 , 2 π ) \theta\in\left[0,\ 2\pi\right) θ ∈ [ 0 , 2 π ) : 4 + 6 cos ⁡ θ = 7 4+6\cos\theta=7 4 + 6 cos θ = 7

θ = π 3 o r 5 π 3 \theta=\frac{\pi}{3}\ or\ \frac{5\pi}{3} θ = 3 π o r 3 5 π

θ = π 6 o r 11 π 6 \theta=\frac{\pi}{6}\ or\ \frac{11\pi}{6} θ = 6 π o r 6 1 1 π

θ = π 6 o r 5 π 6 \theta=\frac{\pi}{6}\ or\ \frac{5\pi}{6} θ = 6 π o r 6 5 π

θ = π 3 o r 2 π 3 \theta=\frac{\pi}{3}\ or\ \frac{2\pi}{3} θ = 3 π o r 3 2 π

Solve for θ ∈ [ 0 , 2 π ) \theta\in\left[0,\ 2\pi\right) θ ∈ [ 0 , 2 π ) : 4 + 6 cos ⁡ θ = 1 4+6\cos\theta=1 4 + 6 cos θ = 1

θ = 2 π 3 o r 4 π 3 \theta=\frac{2\pi}{3}\ or\ \frac{4\pi}{3} θ = 3 2 π o r 3 4 π

θ = 5 π 6 o r 7 π 6 \theta=\frac{5\pi}{6}\ or\ \frac{7\pi}{6} θ = 6 5 π o r 6 7 π

θ = π 3 o r 2 π 3 \theta=\frac{\pi}{3}\ or\ \frac{2\pi}{3} θ = 3 π o r 3 2 π

θ = 7 π 6 o r 11 π 6 \theta=\frac{7\pi}{6}\ or\ \frac{11\pi}{6} θ = 6 7 π o r 6 1 1 π

Solve for θ ∈ [ 0 , 2 π ) \theta\in\left[0,\ 2\pi\right) θ ∈ [ 0 , 2 π ) : 7 − 2 sin ⁡ θ = 6 7-\sqrt{2}\sin\theta=6 7 − 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"> sin θ = 6

θ = π 4 o r 3 π 4 \theta=\frac{\pi}{4}\ or\ \frac{3\pi}{4} θ = 4 π o r 4 3 π

θ = π 2 o r 3 π 2 \theta=\frac{\pi}{2}\ or\ \frac{3\pi}{2} θ = 2 π o r 2 3 π

θ = π 4 o r 7 π 4 \theta=\frac{\pi}{4}\ or\ \frac{7\pi}{4} θ = 4 π o r 4 7 π

θ = 5 π 4 o r 7 π 4 \theta=\frac{5\pi}{4}\ or\ \frac{7\pi}{4} θ = 4 5 π o r 4 7 π

Solve for θ ∈ [ 0 , 2 π ) \theta\in\left[0,\ 2\pi\right) θ ∈ [ 0 , 2 π ) : − 1 + 3 tan ⁡ θ = 2 -1+\sqrt{3}\tan\theta=2 − 1 + 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"> tan θ = 2

θ = π 3 o r 4 π 3 \theta=\frac{\pi}{3}\ or\ \frac{4\pi}{3} θ = 3 π o r 3 4 π

θ = π 3 o r 5 π 3 \theta=\frac{\pi}{3}\ or\ \frac{5\pi}{3} θ = 3 π o r 3 5 π

θ = π 6 o r 5 π 6 \theta=\frac{\pi}{6}\ or\ \frac{5\pi}{6} θ = 6 π o r 6 5 π

θ = π 6 o r 7 π 6 \theta=\frac{\pi}{6}\ or\ \frac{7\pi}{6} θ = 6 π o r 6 7 π

Solve for θ ∈ [ 0 , 2 π ) \theta\in\left[0,\ 2\pi\right) θ ∈ [ 0 , 2 π ) : 3 sin ⁡ θ = − 3 2 \sqrt{3}\sin\theta=-\frac{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"> sin θ = − 2 3

θ = 4 π 3 o r 5 π 3 \theta=\frac{4\pi}{3}\ or\ \frac{5\pi}{3} θ = 3 4 π o r 3 5 π

θ = 7 π 6 o r 11 π 6 \theta=\frac{7\pi}{6}\ or\ \frac{11\pi}{6} θ = 6 7 π o r 6 1 1 π

θ = 2 π 3 o r 4 π 3 \theta=\frac{2\pi}{3}\ or\ \frac{4\pi}{3} θ = 3 2 π o r 3 4 π

θ = 5 π 6 o r 7 π 6 \theta=\frac{5\pi}{6}\ or\ \frac{7\pi}{6} θ = 6 5 π o r 6 7 π

Solve for θ ∈ [ 0 , 2 π ) \theta\in\left[0,\ 2\pi\right) θ ∈ [ 0 , 2 π ) : 3 cos ⁡ θ + 4.5 = 3 \sqrt{3}\cos\theta+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 θ + 4 . 5 = 3

θ = 5 π 6 o r 7 π 6 \theta=\frac{5\pi}{6}\ or\ \frac{7\pi}{6} θ = 6 5 π o r 6 7 π

θ = 4 π 3 o r 5 π 3 \theta=\frac{4\pi}{3}\ or\ \frac{5\pi}{3} θ = 3 4 π o r 3 5 π

θ = 7 π 6 o r 11 π 6 \theta=\frac{7\pi}{6}\ or\ \frac{11\pi}{6} θ = 6 7 π o r 6 1 1 π

θ = 2 π 3 o r 4 π 3 \theta=\frac{2\pi}{3}\ or\ \frac{4\pi}{3} θ = 3 2 π o r 3 4 π

Solve for θ ∈ [ 0 , 2 π ) \theta\in\left[0,\ 2\pi\right) θ ∈ [ 0 , 2 π ) : 2 tan ⁡ θ + 7 = 5 2\tan\theta+7=5 2 tan θ + 7 = 5

θ = 3 π 4 o r 7 π 4 \theta=\frac{3\pi}{4}\ or\ \frac{7\pi}{4} θ = 4 3 π o r 4 7 π

θ = 3 π 4 o r 5 π 4 \theta=\frac{3\pi}{4}\ or\ \frac{5\pi}{4} θ = 4 3 π o r 4 5 π

θ = π 4 o r 5 π 4 \theta=\frac{\pi}{4}\ or\ \frac{5\pi}{4} θ = 4 π o r 4 5 π

θ = 5 π 4 o r 7 π 4 \theta=\frac{5\pi}{4}\ or\ \frac{7\pi}{4} θ = 4 5 π o r 4 7 π

Solve for θ ∈ [ 0 , 2 π ) \theta\in\left[0,\ 2\pi\right) θ ∈ [ 0 , 2 π ) : 2 cos ⁡ θ = − 2 2\cos\theta=-\sqrt{2} 2 cos θ = − 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">

θ = 3 π 4 o r 5 π 4 \theta=\frac{3\pi}{4}\ or\ \frac{5\pi}{4} θ = 4 3 π o r 4 5 π

θ = 3 π 4 o r 7 π 4 \theta=\frac{3\pi}{4}\ or\ \frac{7\pi}{4} θ = 4 3 π o r 4 7 π

θ = π 4 o r 5 π 4 \theta=\frac{\pi}{4}\ or\ \frac{5\pi}{4} θ = 4 π o r 4 5 π

θ = 5 π 4 o r 7 π 4 \theta=\frac{5\pi}{4}\ or\ \frac{7\pi}{4} θ = 4 5 π o r 4 7 π

Solve for θ ∈ [ 0 , 2 π ) \theta\in\left[0,\ 2\pi\right) θ ∈ [ 0 , 2 π ) : 12 sin ⁡ θ + 7 = 1 12\sin\theta+7=1 1 2 sin θ + 7 = 1

θ = 7 π 6 o r 11 π 6 \theta=\frac{7\pi}{6}\ or\ \frac{11\pi}{6} θ = 6 7 π o r 6 1 1 π

θ = 4 π 3 o r 5 π 3 \theta=\frac{4\pi}{3}\ or\ \frac{5\pi}{3} θ = 3 4 π o r 3 5 π

θ = 2 π 3 o r 4 π 3 \theta=\frac{2\pi}{3}\ or\ \frac{4\pi}{3} θ = 3 2 π o r 3 4 π

θ = 5 π 6 o r 7 π 6 \theta=\frac{5\pi}{6}\ or\ \frac{7\pi}{6} θ = 6 5 π o r 6 7 π

Solve for θ ∈ [ 0 , 2 π ) \theta\in\left[0,\ 2\pi\right) θ ∈ [ 0 , 2 π ) : 3 tan ⁡ x + 5 = 4 \sqrt{3}\tan x+5=4 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"> tan x + 5 = 4

θ = 5 π 6 o r 11 π 6 \theta=\frac{5\pi}{6}\ or\ \frac{11\pi}{6} θ = 6 5 π o r 6 1 1 π

θ = 4 π 3 o r 5 π 3 \theta=\frac{4\pi}{3}\ or\ \frac{5\pi}{3} θ = 3 4 π o r 3 5 π

θ = 7 π 6 o r 11 π 6 \theta=\frac{7\pi}{6}\ or\ \frac{11\pi}{6} θ = 6 7 π o r 6 1 1 π

θ = π 3 o r 4 π 3 \theta=\frac{\pi}{3}\ or\ \frac{4\pi}{3} θ = 3 π o r 3 4 π

Solving Trig Equations

Authored by Charlie Burrus

Mathematics

9th - 12th Grade

CCSS covered

Used 42+ times

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10 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$4+6\cos\theta=7$

$\theta=\frac{\pi}{3}\ or\ \frac{5\pi}{3}$

$\theta=\frac{\pi}{6}\ or\ \frac{11\pi}{6}$

$\theta=\frac{\pi}{6}\ or\ \frac{5\pi}{6}$

$\theta=\frac{\pi}{3}\ or\ \frac{2\pi}{3}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$4+6\cos\theta=1$

$\theta=\frac{2\pi}{3}\ or\ \frac{4\pi}{3}$

$\theta=\frac{5\pi}{6}\ or\ \frac{7\pi}{6}$

$\theta=\frac{\pi}{3}\ or\ \frac{2\pi}{3}$

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$7-\sqrt{2}\sin\theta=6$

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

$\theta=\frac{\pi}{2}\ or\ \frac{3\pi}{2}$

$\theta=\frac{\pi}{4}\ or\ \frac{7\pi}{4}$

$\theta=\frac{5\pi}{4}\ or\ \frac{7\pi}{4}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$-1+\sqrt{3}\tan\theta=2$

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

$\theta=\frac{\pi}{3}\ or\ \frac{5\pi}{3}$

$\theta=\frac{\pi}{6}\ or\ \frac{5\pi}{6}$

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$\sqrt{3}\sin\theta=-\frac{3}{2}$

$\theta=\frac{4\pi}{3}\ or\ \frac{5\pi}{3}$

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

$\theta=\frac{2\pi}{3}\ or\ \frac{4\pi}{3}$

$\theta=\frac{5\pi}{6}\ or\ \frac{7\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$\sqrt{3}\cos\theta+4.5=3$

$\theta=\frac{4\pi}{3}\ or\ \frac{5\pi}{3}$

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

$\theta=\frac{2\pi}{3}\ or\ \frac{4\pi}{3}$

$\theta=\frac{5\pi}{6}\ or\ \frac{7\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$2\tan\theta+7=5$

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

$\theta=\frac{3\pi}{4}\ or\ \frac{5\pi}{4}$

$\theta=\frac{\pi}{4}\ or\ \frac{5\pi}{4}$

$\theta=\frac{5\pi}{4}\ or\ \frac{7\pi}{4}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$2\cos\theta=-\sqrt{2}$

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

$\theta=\frac{3\pi}{4}\ or\ \frac{5\pi}{4}$

$\theta=\frac{\pi}{4}\ or\ \frac{5\pi}{4}$

$\theta=\frac{5\pi}{4}\ or\ \frac{7\pi}{4}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$12\sin\theta+7=1$

$\theta=\frac{4\pi}{3}\ or\ \frac{5\pi}{3}$

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

$\theta=\frac{2\pi}{3}\ or\ \frac{4\pi}{3}$

$\theta=\frac{5\pi}{6}\ or\ \frac{7\pi}{6}$

Tags

CCSS.HSF.TF.B.7

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$\sqrt{3}\tan x+5=4$

$\theta=\frac{4\pi}{3}\ or\ \frac{5\pi}{3}$

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

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

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

Tags

CCSS.HSF.TF.B.7

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Solving Trig Equations

Solve for θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right)θ∈[0, 2π) : 4+6cos⁡θ=74+6\cos\theta=74+6cosθ=7

Solve for θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right)θ∈[0, 2π) : 4+6cos⁡θ=14+6\cos\theta=14+6cosθ=1

Solve for θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right)θ∈[0, 2π) : 7−2sin⁡θ=67-\sqrt{2}\sin\theta=67−2​sinθ=6

Solve for θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right)θ∈[0, 2π) : −1+3tan⁡θ=2-1+\sqrt{3}\tan\theta=2−1+3​tanθ=2

Solve for θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right)θ∈[0, 2π) : 3sin⁡θ=−32\sqrt{3}\sin\theta=-\frac{3}{2}3​sinθ=−23​

Solve for θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right)θ∈[0, 2π) : 3cos⁡θ+4.5=3\sqrt{3}\cos\theta+4.5=33​cosθ+4.5=3

Solve for θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right)θ∈[0, 2π) : 2tan⁡θ+7=52\tan\theta+7=52tanθ+7=5

Solve for θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right)θ∈[0, 2π) : 2cos⁡θ=−22\cos\theta=-\sqrt{2}2cosθ=−2​

Solve for θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right)θ∈[0, 2π) : 12sin⁡θ+7=112\sin\theta+7=112sinθ+7=1

Solve for θ∈[0, 2π)\theta\in\left[0,\ 2\pi\right)θ∈[0, 2π) : 3tan⁡x+5=4\sqrt{3}\tan x+5=43​tanx+5=4

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Discover more resources for Mathematics

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$4+6\cos\theta=7$

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$4+6\cos\theta=1$

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$7-\sqrt{2}\sin\theta=6$

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$-1+\sqrt{3}\tan\theta=2$

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$\sqrt{3}\sin\theta=-\frac{3}{2}$

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$\sqrt{3}\cos\theta+4.5=3$

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$2\tan\theta+7=5$

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$2\cos\theta=-\sqrt{2}$

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$12\sin\theta+7=1$

Solve for $\theta\in\left[0,\ 2\pi\right)$ :
$\sqrt{3}\tan x+5=4$