Given x : [0, 2 π], Solve the following equation: cos ⁡ x = 1 2 \cos\ x\ =\frac{1}{2} cos x = 2 1

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

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

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

Given x : [0, 2 π], Solve the following equation: cos ⁡ x = 0 \cos\ x\ =0 cos x = 0

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

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

x = π , 2 π x\ =\pi\ ,\ \ 2\pi x = π , 2 π

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

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

Given x : [0, 2 π], Solve the following equation: sin ⁡ x = 0 \sin\ x\ =0 sin x = 0

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

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

x = π , 2 π x\ =\pi\ ,\ \ 2\pi x = π , 2 π

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

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

Given x : [0, 2 π], Solve the following equation: sin ⁡ x = − 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">

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

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

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

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

Given x : [0, 2 π], Solve the following equation: sin ⁡ x = − 1 \sin\ x\ =-1 sin x = − 1

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

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

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

x = π , 2 π x\ =\pi\ ,\ \ 2\pi x = π , 2 π

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

Given x : [0, 2 π], Solve the following equation: 2 sin ⁡ x − 3 = 0 2\sin\ x-\sqrt{3}=0 2 sin 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

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

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

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

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

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

Given x : [0, 2 π], Solve the following equation: 12 cos ⁡ x + 6 √ 3 = 0 12\cos x+6√3=0 1 2 cos x + 6 √ 3 = 0

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

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

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

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

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

Given x : [0, 2 π], Solve the following equation: 8 sin ⁡ x + 4 = 0 8\sin x+4=0 8 sin x + 4 = 0

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

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

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

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

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

Given x : [0, 2 π], Solve the following equation: − 10 cos ⁡ x + 6 = 1 -10\cos x+6=1 − 1 0 cos x + 6 = 1

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

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

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

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

Given x : [0, 2 π], Solve the following equation: 14 sin ⁡ x + 7 2 = 0 14\sin x+7\sqrt{2}=0 1 4 sin x + 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"> = 0

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

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

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

x = 3 π 4 , 7 π 4 x\ =\ \frac{3\pi}{4}\ \ ,\ \ \ \frac{7\pi}{4} x = 4 3 π , 4 7 π

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

Given x : [0, 2 π], Solve the following equation: − 16 sin ⁡ x + 8 2 = 0 -16\sin x+8\sqrt{2}=0 − 1 6 sin x + 8 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

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

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

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

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

x = 3 π 4 , 7 π 4 x\ =\ \frac{3\pi}{4}\ \ ,\ \ \ \frac{7\pi}{4} x = 4 3 π , 4 7 π

Given x : [0, 2 π], Solve the following equation: 10 cos ⁡ x − 5 2 = 0 10\cos x-5\sqrt{2}=0 1 0 cos x − 5 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

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

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

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

x = 3 π 4 , 7 π 4 x\ =\ \frac{3\pi}{4}\ \ ,\ \ \ \frac{7\pi}{4} x = 4 3 π , 4 7 π

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

Given x : [0, 2 π], Solve the following equation: 5 sin ⁡ x − 2 = 3 5\sin x\ -2=3 5 sin x − 2 = 3

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

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

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

x = π , 2 π x\ =\pi\ ,\ \ 2\pi x = π , 2 π

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

Given x : [0, 2 π], Solve the following equation: 5 cos ⁡ x + 2 = − 3 5\cos x\ +2=-3 5 cos x + 2 = − 3

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

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

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

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

Given x : [0, 2 π], Solve the following equation: 7 cos ⁡ x − 7 sin ⁡ x = 0 7\cos x-7\sin x=0 7 cos x − 7 sin x = 0

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

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

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

x = 3 π 4 , 7 π 4 x\ =\ \frac{3\pi}{4}\ \ ,\ \ \ \frac{7\pi}{4} x = 4 3 π , 4 7 π

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

Given x : [0, 2 π], Solve the following equation: 2 sin ⁡ x + 2 cos ⁡ x = 0 2\sin x+2\cos x=0 2 sin x + 2 cos x = 0

x = 3 π 4 , 7 π 4 x\ =\ \frac{3\pi}{4}\ \ ,\ \ \ \frac{7\pi}{4} x = 4 3 π , 4 7 π

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

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

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

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

Solving Trigonometric Equations Basic

Authored by Adeyemi Aderinto

Mathematics

10th Grade - University

CCSS covered

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

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

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

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

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

$x\ =\ \frac{2\pi}{3}\ ,\ \ \ \frac{4\pi}{3}$

Tags

CCSS.HSF.TF.B.7

10.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Given x : [0, 2π], Solve the following equation: $14\sin x+7\sqrt{2}=0$

$x\ =\ \frac{5\pi}{4}\ \ ,\ \ \ \frac{7\pi}{4}$

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

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

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

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

Tags

CCSS.HSF.TF.B.7

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Solving Trigonometric Equations Basic

Given x : [0, 2π], Solve the following equation: cos⁡ x =12\cos\ x\ =\frac{1}{2}cos x =21​

Given x : [0, 2π], Solve the following equation: cos⁡ x =0\cos\ x\ =0cos x =0

Given x : [0, 2π], Solve the following equation: sin⁡ x =0\sin\ x\ =0sin x =0

Given x : [0, 2π], Solve the following equation: sin⁡ x =−32\sin\ x\ =-\frac{\sqrt{3}}{2}sin x =−23​​

Given x : [0, 2π], Solve the following equation: sin⁡ x =−1\sin\ x\ =-1sin x =−1

Given x : [0, 2π], Solve the following equation: 2sin⁡ x−3=02\sin\ x-\sqrt{3}=02sin x−3​=0

Given x : [0, 2π], Solve the following equation: 12cos⁡x+6√3=012\cos x+6√3=012cosx+6√3=0

Given x : [0, 2π], Solve the following equation: 8sin⁡x+4=08\sin x+4=08sinx+4=0

Given x : [0, 2π], Solve the following equation: −10cos⁡x+6=1-10\cos x+6=1−10cosx+6=1

Given x : [0, 2π], Solve the following equation: 14sin⁡x+72=014\sin x+7\sqrt{2}=014sinx+72​=0

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Given x : [0, 2π], Solve the following equation: $\sin\ x\ =0$

Given x : [0, 2π], Solve the following equation: $\sin\ x\ =-\frac{\sqrt{3}}{2}$

Given x : [0, 2π], Solve the following equation: $\sin\ x\ =-1$

Given x : [0, 2π], Solve the following equation: $2\sin\ x-\sqrt{3}=0$

Given x : [0, 2π], Solve the following equation: $12\cos x+6√3=0$

Given x : [0, 2π], Solve the following equation: $8\sin x+4=0$

Given x : [0, 2π], Solve the following equation: $-10\cos x+6=1$

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