Solving Trig Equations

Solve: 4sinθ + 1 = 3

State all solutions in the interval [0, 2π)

• π/ 6, 7π/6

• π/6, 5π/ 6

• 5π/6, 7π/6

• 7π/6, 11π/6

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

CCSS.HSF.TF.B.7

Solve: 2cscθ + 2 = 0

State all solutions in the interval [0, 2π)

• π/2, 3π/2

• π/2

• 3π /2

• π

Tags

CCSS.HSF.TF.B.7

Solve:  $2\sqrt{3}\sec\theta\ +\ 4\ =\ 0$ 
State all solutions in the interval [0, 2π)

• π /3,  2π/3

• 2π /3,  4π/3

• π /6,  5π/6

• 5π /6,  7π/6

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

CCSS.HSF.TF.B.7

Solve: 2cosx - 4 = 0

State all solutions in the interval [0, 2π)

• No solution

• π/3, 5π/3

• π/6, 11π/6

• 2π/3, 4π/3

Solve: 4sin²x = 3

State all solutions in the interval [0, 2π)

• π/6, 11π/6

• π/3, 2π/3

• π/6, 5π/6, 7π/6, 11π/6

• π/3, 2π/3, 4π/3, 5π/3

Tags

CCSS.HSA.REI.B.4

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.B.7

Solve equation for  $0\le\theta<2\pi$  .
 $-2+\cot\theta=-3$  

•  $\theta=\frac{3\pi}{4},\frac{4\pi}{3},\frac{7\pi}{4}$  

•  $\theta=\frac{3\pi}{4},\frac{7\pi}{4}$  

•  $\theta=\frac{\pi}{3},\frac{4\pi}{3}$  

•  $\theta=\frac{3\pi}{4},\frac{4\pi}{3}$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSF.TF.B.7

Solve equation for  $0\le\theta<2\pi$  .
 $2=-4-3\csc\theta$  

•  $\theta=\frac{2\pi}{3},\frac{7\pi}{6}$  

•  $\theta=\frac{\pi}{3}$  

•  $\theta=\frac{7\pi}{6},\frac{11\pi}{6}$  

•  $\theta=\frac{2\pi}{3},\frac{7\pi}{6},\frac{11\pi}{6}$  

Tags

CCSS.HSF.TF.B.7

Solve equation for  $0\le\theta<2\pi$  .
 $-1-2\sec^2\theta=-3\sec^2\theta$  

•  $\theta=0,\pi,\frac{4\pi}{3}$  

•  $\theta=0$  

•  $\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$  

•  $\theta=0,\pi$  

Tags

CCSS.HSF.TF.B.7

Solve equation for  $0\le\theta<2\pi$  .
 $3\tan^2\theta\ -1\ =\ 0$  

•  $\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$  

•  $\theta=\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$  

•  $\theta=\frac{\pi}{6},\frac{7\pi}{6}$  

•  $\theta=\frac{\pi}{3},\frac{4\pi}{3}$  

Tags

CCSS.HSA.REI.B.4

CCSS.HSF.TF.A.3

Solve equation for  $0\le\theta<2\pi$  .
 $6\tan\theta\ +\ 6\sqrt{3}\ =\ 0$  

•  $\theta=\frac{\pi}{6},\frac{7\pi}{6}$  

•  $\theta=\frac{5\pi}{6},\frac{11\pi}{6}$  

•  $\theta=\frac{\pi}{3},\frac{4\pi}{3}$  

•  $\theta=\frac{2\pi}{3},\frac{5\pi}{3}$  

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

CCSS.HSF.TF.B.7