The solution set of the equation sin ⁡ x = − 1 2 \sin x=-\frac{1}{2} sin x = − 2 1 for < 0 , 2 π > <0,2\pi> < 0 , 2 π > is:

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

{ 7 π 6 } \left\{\frac{7\pi}{6}\right\} { 6 7 π }

{ 11 π 6 } \left\{\frac{11\pi}{6}\right\} { 6 1 1 π }

{ 5 π 6 , 7 π 6 } \left\{\frac{5\pi}{6},\frac{7\pi}{6}\right\} { 6 5 π , 6 7 π }

The solution set of the equation 2 t g x − 2 cot ⁡ g x + 3 = 0 2tgx-2\cot gx+3=0 2 t g x − 2 cot g x + 3 = 0 is:

{ 26 , 6 ° + 180 k ; 116 , 6 ° + 180 k } \left\{26,6\degree+180k;\ 116,6\degree+180k\right\} { 2 6 , 6 ° + 1 8 0 k ; 1 1 6 , 6 ° + 1 8 0 k }

{ 63 , 4 ° + 180 k ; 153 , 4 ° + 180 k } \left\{63,4\degree+180k;\ 153,4\degree+180k\right\} { 6 3 , 4 ° + 1 8 0 k ; 1 5 3 , 4 ° + 1 8 0 k }

{ 26 , 6 ° + 180 k } \left\{26,6\degree+180k\right\} { 2 6 , 6 ° + 1 8 0 k }

{ 153 , 4 ° + 180 k } \left\{153,4\degree+180k\right\} { 1 5 3 , 4 ° + 1 8 0 k }

The solution set of the equation cos ⁡ ( 2 x − π ) = − 1 \cos\left(2x-\pi\right)=-1 cos ( 2 x − π ) = − 1 for < 0 , 2 π > <0,2\pi> < 0 , 2 π > is

{ 0 , 180 , 360 } \left\{0,180,360\right\} { 0 , 1 8 0 , 3 6 0 }

{ 0 , 360 } \left\{0,360\right\} { 0 , 3 6 0 }

{ 0 , 180 } \left\{0,180\right\} { 0 , 1 8 0 }

{ 180 , 360 } \left\{180,360\right\} { 1 8 0 , 3 6 0 }

The solution set of the equation cos ⁡ ( x 4 ) = 0 , 4 \cos\left(\frac{x}{4}\right)=0,4 cos ( 4 x ) = 0 , 4 is:

{ 66 , 4 ° + 360 k ; 293 , 6 ° + 360 k } \left\{66,4\degree+360k;\ 293,6\degree+360k\right\} { 6 6 , 4 ° + 3 6 0 k ; 2 9 3 , 6 ° + 3 6 0 k }

{ 265 , 6 ° + 360 k ; 1174 , 4 ° + 360 k } \left\{265,6\degree+360k;\ 1174,4\degree+360k\right\} { 2 6 5 , 6 ° + 3 6 0 k ; 1 1 7 4 , 4 ° + 3 6 0 k }

{ 66 , 4 ° + 1440 k ; 293 , 6 ° + 1440 k } \left\{66,4\degree+1440k;\ 293,6\degree+1440k\right\} { 6 6 , 4 ° + 1 4 4 0 k ; 2 9 3 , 6 ° + 1 4 4 0 k }

The solution set of the equation sin ⁡ ( 60 + 3 x ) = − 2 2 \sin\left(60+3x\right)=-\frac{\sqrt{2}}{2} sin ( 6 0 + 3 x ) = − 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"> is:

{ 55 ° + 360 k ; 85 ° + 360 k } \left\{55\degree+360k;\ 85\degree+360k\right\} { 5 5 ° + 3 6 0 k ; 8 5 ° + 3 6 0 k }

{ 225 ° + 120 k ; 315 ° + 120 k } \left\{225\degree+120k;\ 315\degree+120k\right\} { 2 2 5 ° + 1 2 0 k ; 3 1 5 ° + 1 2 0 k }

{ 55 ° + 120 k ; 85 ° + 120 k } \left\{55\degree+120k;\ 85\degree+120k\right\} { 5 5 ° + 1 2 0 k ; 8 5 ° + 1 2 0 k }

{ 165 ° + 360 k ; 255 ° + 360 k } \left\{165\degree+360k;\ 255\degree+360k\right\} { 1 6 5 ° + 3 6 0 k ; 2 5 5 ° + 3 6 0 k }

{ 225 ° + 360 k ; 315 ° + 360 k } \left\{225\degree+360k;\ 315\degree+360k\right\} { 2 2 5 ° + 3 6 0 k ; 3 1 5 ° + 3 6 0 k }

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Math

Trigonometry

Trigonometric Equations

trigonometric equations

Authored by Majka Čam

Mathematics

10th Grade

CCSS covered

Used 15+ times

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10 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The solution set of the equation $\sin x=-\frac{1}{2}$
for $<0,2\pi>$ is:

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

$\left\{\frac{7\pi}{6}\right\}$

$\left\{\frac{11\pi}{6}\right\}$

$\left\{\frac{5\pi}{6},\frac{7\pi}{6}\right\}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many solutions does the following equation have? $\cos^2x+3\cos x=\sin^2x-2$ for $<-180,540>$

Tags

CCSS.HSF.TF.B.7

FILL IN THE BLANKS QUESTION

1 min • 1 pt

The following equation has for $<0;90>$ solutions $x_1$ and $x_2$ . Find the sum of $x_1$ and $x_2$ .

$\sin2x=\cos x$

(a)

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The solution set of the equation $2tgx-2\cot gx+3=0$ is:

$\left\{26,6\degree+180k;\ 116,6\degree+180k\right\}$

$\left\{63,4\degree+180k;\ 153,4\degree+180k\right\}$

$\left\{26,6\degree+180k\right\}$

$\left\{153,4\degree+180k\right\}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The solution set of the equation $\cos\left(2x-\pi\right)=-1$ for $<0,2\pi>$ is

$\left\{0,180,360\right\}$

$\left\{0,360\right\}$

$\left\{0,180\right\}$

$\left\{180,360\right\}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The solution set of the equation $\cos\left(\frac{x}{4}\right)=0,4$ is:

$\left\{66,4\degree+360k;\ 293,6\degree+360k\right\}$

$\left\{265,6\degree+1440k;\ 1174,4\degree+1440k\right\}$

$\left\{265,6\degree+360k;\ 1174,4\degree+360k\right\}$

$\left\{66,4\degree+1440k;\ 293,6\degree+1440k\right\}$

Tags

CCSS.HSF.TF.B.7

FILL IN THE BLANKS QUESTION

1 min • 1 pt

The following equation has for $<0;360>$ solutions $x_1$ and $x_2$ . Find the sum of $x_1$ and $x_2$ .

$7tgx=15$

(a)

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The solution set of the equation $\sin\left(60+3x\right)=-\frac{\sqrt{2}}{2}$ is:

$\left\{225\degree+120k;\ 315\degree+120k\right\}$

$\left\{55\degree+360k;\ 85\degree+360k\right\}$

$\left\{55\degree+120k;\ 85\degree+120k\right\}$

$\left\{165\degree+360k;\ 255\degree+360k\right\}$

$\left\{225\degree+360k;\ 315\degree+360k\right\}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The solution set of the equation $\sin^2x+2\sin x-3=0$ for $<-2\pi,2\pi>$ is

$\left\{90\degree\right\}$

$\left\{-270\degree,90\degree\right\}$

$\left\{270\degree\right\}$

$\left\{-270\degree\right\}$

$\left\{-90\degree,\ 270\degree\right\}$

Tags

CCSS.HSF.TF.B.7

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many solutions does the following equation have? $2\cos^2x+3\cos x=9$ .

$\infty$

Tags

CCSS.HSF.TF.B.7

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trigonometric equations

The solution set of the equation sin⁡x=−12\sin x=-\frac{1}{2}sinx=−21​ for <0,2π><0,2\pi><0,2π> is:

How many solutions does the following equation have? cos⁡2x+3cos⁡x=sin⁡2x−2\cos^2x+3\cos x=\sin^2x-2cos2x+3cosx=sin2x−2 for <−180,540><-180,540><−180,540>

The following equation has for <0;90><0;90><0;90> solutions x1x_1x1​ and x2x_2x2​ . Find the sum of x1x_1x1​ and x2x_2x2​ . sin⁡2x=cos⁡x\sin2x=\cos xsin2x=cosx (a)

The solution set of the equation 2tgx−2cot⁡gx+3=02tgx-2\cot gx+3=02tgx−2cotgx+3=0 is:

The solution set of the equation cos⁡(2x−π)=−1\cos\left(2x-\pi\right)=-1cos(2x−π)=−1 for <0,2π><0,2\pi><0,2π> is

The solution set of the equation cos⁡(x4)=0,4\cos\left(\frac{x}{4}\right)=0,4cos(4x​)=0,4 is:

The following equation has for <0;360><0;360><0;360> solutions x1x_1x1​ and x2x_2x2​ . Find the sum of x1x_1x1​ and x2x_2x2​ . 7tgx=157tgx=157tgx=15 (a)

The solution set of the equation sin⁡(60+3x)=−22\sin\left(60+3x\right)=-\frac{\sqrt{2}}{2}sin(60+3x)=−22​​ is:

The solution set of the equation sin⁡2x+2sin⁡x−3=0\sin^2x+2\sin x-3=0sin2x+2sinx−3=0 for <−2π,2π><-2\pi,2\pi><−2π,2π> is

How many solutions does the following equation have? 2cos⁡2x+3cos⁡x=92\cos^2x+3\cos x=92cos2x+3cosx=9 .

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Discover more resources for Mathematics

The solution set of the equation $\sin x=-\frac{1}{2}$
for $<0,2\pi>$ is:

How many solutions does the following equation have? $\cos^2x+3\cos x=\sin^2x-2$ for $<-180,540>$

The following equation has for $<0;90>$ solutions $x_1$ and $x_2$ . Find the sum of $x_1$ and $x_2$ .

$\sin2x=\cos x$

(a)

The solution set of the equation $2tgx-2\cot gx+3=0$ is:

The solution set of the equation $\cos\left(2x-\pi\right)=-1$ for $<0,2\pi>$ is

The solution set of the equation $\cos\left(\frac{x}{4}\right)=0,4$ is:

The following equation has for $<0;360>$ solutions $x_1$ and $x_2$ . Find the sum of $x_1$ and $x_2$ .

$7tgx=15$

(a)

The solution set of the equation $\sin\left(60+3x\right)=-\frac{\sqrt{2}}{2}$ is:

The solution set of the equation $\sin^2x+2\sin x-3=0$ for $<-2\pi,2\pi>$ is

How many solutions does the following equation have? $2\cos^2x+3\cos x=9$ .