Solve the trigonometric equation in the interval ( 0 , 2 π ] \left(0,\ 2\pi\right] ( 0 , 2 π ] . 2 2 csc ⁡ x − 1 = 0 \frac{\sqrt{2}}{2}\csc x-1=0 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"> csc x − 1 = 0

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

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

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

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

Solve the trigonometric equation in the interval ( 0 , 2 π ] \left(0,\ 2\pi\right] ( 0 , 2 π ] . 11 sin ⁡ x + 5 = sin ⁡ x 11\sin x+5=\sin x 1 1 sin x + 5 = sin x

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

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

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

π 6 , 5 π 6 , 7 π 6 , 11 π 6 \frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6} 6 π , 6 5 π , 6 7 π , 6 1 1 π

Solve the trigonometric equation in the interval ( 0 , 2 π ] \left(0,\ 2\pi\right] ( 0 , 2 π ] . cos ⁡ x + sin ⁡ x tan ⁡ x = 2 \cos x+\sin x\tan x=2 cos x + sin x tan x = 2

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

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

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

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

Solve the trigonometric equation in the interval ( 0 , 2 π ] \left(0,\ 2\pi\right] ( 0 , 2 π ] . 2 sin ⁡ 3 x + 3 = 0 2\sin3x+\sqrt{3}=0 2 sin 3 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

4 π 9 , 5 π 9 \frac{4\pi}{9},\frac{5\pi}{9} 9 4 π , 9 5 π

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

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

π 6 , 4 π 9 , 2 π 9 , 5 π 9 \frac{\pi}{6},\frac{4\pi}{9},\frac{2\pi}{9},\frac{5\pi}{9} 6 π , 9 4 π , 9 2 π , 9 5 π

[YEAR 11 MATHEMATICS]: Solving Trigonometric Equations

Authored by Kevin Corke

Mathematics

11th - 12th Grade

CCSS covered

Used 3+ times

[YEAR 11 MATHEMATICS]: Solving Trigonometric Equations

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10 questions

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MULTIPLE CHOICE QUESTION

5 mins • 5 pts

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$\frac{\sqrt{2}}{2}\csc x-1=0$

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

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

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

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

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$11\sin x+5=\sin x$

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

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

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

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$100\cos^2x-25=0$

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

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

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

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE SELECT QUESTION

5 mins • 1 pt

Which of the following are the correct solutions for the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ ?

CHOOSE ALL THAT APPLY

$\left(2\sin^2x-1\right)\left(3\tan^2x-1\right)=0$

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

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

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

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$9\tan^3x=3\tan x$

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

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

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

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE SELECT QUESTION

5 mins • 1 pt

Which of the following are the correct solutions for the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ ?

CHOOSE ALL THAT APPLY

$14\sin^2x+21\sin x+7=0$

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

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

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

$\frac{\pi}{2}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$\cos x+\sin x\tan x=2$

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

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

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

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$50\sin^2x=50+25\cos x$

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

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

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

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

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$2\sin3x+\sqrt{3}=0$

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

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

$\frac{4\pi}{9},\frac{5\pi}{9}$

$\frac{\pi}{6},\frac{4\pi}{9},\frac{2\pi}{9},\frac{5\pi}{9}$

Tags

CCSS.HSF.TF.B.7

10.

MULTIPLE SELECT QUESTION

5 mins • 1 pt

Which of the following are the correct solutions for the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ ?

CHOOSE ALL THAT APPLY

$\cos x=0$

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

$\pi$

$2\pi$

$\frac{\pi}{2}$

Tags

CCSS.HSF.TF.B.7

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[YEAR 11 MATHEMATICS]: Solving Trigonometric Equations

Solve the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] . 22csc⁡x−1=0\frac{\sqrt{2}}{2}\csc x-1=022​​cscx−1=0

Solve the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] . 11sin⁡x+5=sin⁡x11\sin x+5=\sin x11sinx+5=sinx

Solve the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] . 100cos⁡2x−25=0100\cos^2x-25=0100cos2x−25=0

Which of the following are the correct solutions for the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] ? CHOOSE ALL THAT APPLY (2sin⁡2x−1)(3tan⁡2x−1)=0\left(2\sin^2x-1\right)\left(3\tan^2x-1\right)=0(2sin2x−1)(3tan2x−1)=0

Solve the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] . 9tan⁡3x=3tan⁡x9\tan^3x=3\tan x9tan3x=3tanx

Which of the following are the correct solutions for the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] ? CHOOSE ALL THAT APPLY 14sin⁡2x+21sin⁡x+7=014\sin^2x+21\sin x+7=014sin2x+21sinx+7=0

Solve the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] . cos⁡x+sin⁡xtan⁡x=2\cos x+\sin x\tan x=2cosx+sinxtanx=2

Solve the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] . 50sin⁡2x=50+25cos⁡x50\sin^2x=50+25\cos x50sin2x=50+25cosx

Solve the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] . 2sin⁡3x+3=02\sin3x+\sqrt{3}=02sin3x+3​=0

Which of the following are the correct solutions for the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] ? CHOOSE ALL THAT APPLY cos⁡x=0\cos x=0cosx=0

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Discover more resources for Mathematics

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$\frac{\sqrt{2}}{2}\csc x-1=0$

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$11\sin x+5=\sin x$

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$100\cos^2x-25=0$

Which of the following are the correct solutions for the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ ?

CHOOSE ALL THAT APPLY

$\left(2\sin^2x-1\right)\left(3\tan^2x-1\right)=0$

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$9\tan^3x=3\tan x$

Which of the following are the correct solutions for the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ ?

CHOOSE ALL THAT APPLY

$14\sin^2x+21\sin x+7=0$

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$\cos x+\sin x\tan x=2$

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$50\sin^2x=50+25\cos x$

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$2\sin3x+\sqrt{3}=0$

Which of the following are the correct solutions for the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ ?

CHOOSE ALL THAT APPLY

$\cos x=0$