3 sin ⁡ x + 1 = sin ⁡ x 3\sin\ x\ +\ 1\ =\ \sin\ x 3 sin x + 1 = sin x

x = 7 π 6 + 2 π n , x = 11 π 6 + 2 π n x=\frac{7\pi}{6}+2\pi n,\ \ \ x\ =\ \frac{11\pi}{6}+2\pi n x = 6 7 π + 2 π n , x = 6 1 1 π + 2 π n

x = π 6 + 2 π n , x = 5 π 6 + 2 π n x=\frac{\pi}{6}+2\pi n,\ \ \ x\ =\ \frac{5\pi}{6}+2\pi n x = 6 π + 2 π n , x = 6 5 π + 2 π n

x = 4 π 3 + 2 π n , x = 5 π 3 + 2 π n x=\frac{4\pi}{3}+2\pi n,\ \ \ \ x=\frac{5\pi}{3}+2\pi n x = 3 4 π + 2 π n , x = 3 5 π + 2 π n

x = π 4 + π n x=\frac{\pi}{4}+\pi n x = 4 π + π n

Solve equation for 0 ≤ θ < 2 π 0\le\theta<2\pi 0 ≤ θ < 2 π . 1 = 5 − 8 cos ⁡ θ 1=5-8\cos\theta 1 = 5 − 8 cos θ

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

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

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

θ = π 6 \theta=\frac{\pi}{6} θ = 6 π

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 . − sin ⁡ θ csc ⁡ θ + 3 csc ⁡ θ = 2 sin ⁡ θ + 3 csc ⁡ θ -\sin\theta\csc\theta+3\csc\theta=\sqrt{2}\sin\theta+3\csc\theta − sin θ csc θ + 3 csc 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"> sin θ + 3 csc θ

θ = 5 π 4 , 7 π 4 \theta=\frac{5\pi}{4},\frac{7\pi}{4} θ = 4 5 π , 4 7 π

θ = 5 π 4 , 11 π 6 \theta=\frac{5\pi}{4},\frac{11\pi}{6} θ = 4 5 π , 6 1 1 π

θ = 3 π 4 , 7 π 6 , 7 π 4 \theta=\frac{3\pi}{4},\frac{7\pi}{6},\frac{7\pi}{4} θ = 4 3 π , 6 7 π , 4 7 π

θ = 0 , π , 5 π 4 , 7 π 4 \theta=0,\pi,\frac{5\pi}{4},\frac{7\pi}{4} θ = 0 , π , 4 5 π , 4 7 π

Find the solution on the interval [0, 2π)

0; π; π/4; 3π/4; 5π/4; 7π/4

Find the solution over the interval [0, 2π)

0, π, π/6, 5π/6, 7π/6, 11π/6

Solving Trig Equations

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HSF.TF.B.7

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Jennifer Gray

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