Solve the trigonometric equation: 2 cos ⁡ ( x ) + 2 = 0 2\cos\left(x\right)+\sqrt{2}=0 2 cos ( x ) + 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

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

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

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

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

Solve the following trigonometric equation: sec ⁡ ( x ) + 2 = 0 \sec\left(x\right)+2=0 sec ( x ) + 2 = 0

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

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

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

Solve the trigonometric equation: sec ⁡ ( x ) csc ⁡ ( x ) − 2 sec ⁡ ( x ) + csc ⁡ ( x ) = csc ⁡ ( x ) \sec\left(x\right)\csc\left(x\right)-2\sec\left(x\right)+\csc\left(x\right)=\csc\left(x\right) sec ( x ) csc ( x ) − 2 sec ( x ) + csc ( x ) = csc ( x )

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

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

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

The value of sin ⁡ − 1 ( − 1 2 ) \sin^{-1}\left(-\frac{1}{2}\right)\ sin − 1 ( − 2 1 )

− π 6 -\frac{\pi}{6} − 6 π

− π 3 -\frac{\pi}{3} − 3 π

The value of cos ⁡ − 1 ( − 3 2 ) \cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\ cos − 1 ( − 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"> ) is

− 5 π 6 -\frac{5\pi}{6} − 6 5 π

− π 6 -\frac{\pi}{6} − 6 π

Find the exact value of cos ⁡ − 1 ( 3 2 ) \cos^{-1}\left(\frac{\sqrt{3}}{2}\right) cos − 1 ( 2 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" /> )

− π 3 -\frac{\pi}{3} − 3 π

− π 6 -\frac{\pi}{6} − 6 π

Find the exact value of sec ⁡ − 1 ( − 2 ) \sec^{-1}\left(-2\right) sec − 1 ( − 2 )

− π 3 -\frac{\pi}{3} − 3 π

− 2 π 3 -\frac{2\pi}{3} − 3 2 π

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Trigonometric Equations

Pre Calculus: Solving Trigonometric Equations

Pre-Calculus: Solving Trigonometric Equations

Authored by Haneen Sayyad

Mathematics

10th - 12th Grade

CCSS covered

Used 62+ times

Pre-Calculus: Solving Trigonometric Equations

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14 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\frac{\pi}{6}$ is a possible solution to the equation $2\sin^2\alpha+3\sin\alpha-2=0$

True

False

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve the trigonometric equation:
$4\sin^2\left(x\right)-3=0$

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

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

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

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve the trigonometric equation:
$2\cos\left(x\right)+\sqrt{2}=0$

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

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

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

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve the following trigonometric equation:
$\sec\left(x\right)+2=0$

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

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

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

$0,\pi$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve the trigonometric function:
$-2-3\sin\left(x\right)=1-6\sin\left(x\right)$

$0$

$\frac{3\pi}{2}$

$\frac{\pi}{2}$

$\frac{\pi}{4}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve the trigonometric equation:

$\tan^2\left(x\right)+2\tan\left(x\right)=-1$

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

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

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

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve the trigonometric equation:
$\sec\left(x\right)\csc\left(x\right)-2\sec\left(x\right)+\csc\left(x\right)=\csc\left(x\right)$

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

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

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

$0,\pi$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The value of $\sin^{-1}\left(-\frac{1}{2}\right)\$

$\frac{\pi}{3}$

$\frac{\pi}{6}$

$-\frac{\pi}{3}$

$-\frac{\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The value of $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\$ is

$\frac{5\pi}{6}$

$-\frac{5\pi}{6}$

$\frac{\pi}{6}$

$-\frac{\pi}{6}$

Tags

CCSS.HSF.TF.B.7

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Pre-Calculus: Solving Trigonometric Equations

π6\frac{\pi}{6}6π​ is a possible solution to the equation 2sin⁡2α+3sin⁡α−2=02\sin^2\alpha+3\sin\alpha-2=02sin2α+3sinα−2=0

Solve the trigonometric equation: 4sin⁡2(x)−3=04\sin^2\left(x\right)-3=04sin2(x)−3=0

Solve the trigonometric equation: 2cos⁡(x)+2=02\cos\left(x\right)+\sqrt{2}=02cos(x)+2​=0

Solve the following trigonometric equation: sec⁡(x)+2=0\sec\left(x\right)+2=0sec(x)+2=0

Solve the trigonometric function: −2−3sin⁡(x)=1−6sin⁡(x)-2-3\sin\left(x\right)=1-6\sin\left(x\right)−2−3sin(x)=1−6sin(x)

Solve the trigonometric equation: tan⁡2(x)+2tan⁡(x)=−1\tan^2\left(x\right)+2\tan\left(x\right)=-1tan2(x)+2tan(x)=−1

Solve the trigonometric equation: sec⁡(x)csc⁡(x)−2sec⁡(x)+csc⁡(x)=csc⁡(x)\sec\left(x\right)\csc\left(x\right)-2\sec\left(x\right)+\csc\left(x\right)=\csc\left(x\right)sec(x)csc(x)−2sec(x)+csc(x)=csc(x)

The value of sin⁡−1(−12) \sin^{-1}\left(-\frac{1}{2}\right)\ sin−1(−21​)

The value of cos⁡−1(−32) \cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\ cos−1(−23​​) is

csc-1(-√(2))

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Discover more resources for Mathematics

$\frac{\pi}{6}$ is a possible solution to the equation $2\sin^2\alpha+3\sin\alpha-2=0$

Solve the trigonometric equation:
$4\sin^2\left(x\right)-3=0$

Solve the trigonometric equation:
$2\cos\left(x\right)+\sqrt{2}=0$

Solve the following trigonometric equation:
$\sec\left(x\right)+2=0$

Solve the trigonometric function:
$-2-3\sin\left(x\right)=1-6\sin\left(x\right)$

Solve the trigonometric equation:

$\tan^2\left(x\right)+2\tan\left(x\right)=-1$

Solve the trigonometric equation:
$\sec\left(x\right)\csc\left(x\right)-2\sec\left(x\right)+\csc\left(x\right)=\csc\left(x\right)$

The value of $\sin^{-1}\left(-\frac{1}{2}\right)\$

The value of $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\$ is

csc^-1(-√(2))