Solving Trig Equations

Solve
cos²θ = ½ 
on θ∈[0, 2π)

• θ = π /4, 7π /4
• θ = π /4, 3π /4
• θ = 3π /4, 5π /4
• θ = π /4, 3π /4, 5π /4, 7π /4

Tags

CCSS.HSF.TF.B.7

• No solution
• π/3 +2πn, 5π/3 +2πn
• π/6 +2πn, 11π/6 +2πn
• 2π/3 +2πn, 4π/3 +2πn

Tags

CCSS.HSF.TF.B.7

Solve on the domain [0, 2π)
cos² x + sin x + 1 = 0

• π
• 3π/2
• π/6, 5π/6, 3π/2
• No solution

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  $0\le\theta<2\pi$  .
 $1+\tan^2\theta=4\tan^2\theta$  

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

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

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

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

Tags

CCSS.HSF.TF.B.7

Solve equation for  $0\le\theta<2\pi$  .
 $0=-\sqrt{3}\sin\theta-2\sin^2\theta$  

•  $\theta=0,\frac{2\pi}{3},\pi,\frac{5\pi}{3}$  

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

•  $\theta=0,\pi,\frac{4\pi}{3},\frac{5\pi}{3}$  

•  $\theta=0,\pi,\frac{5\pi}{3}$  

Tags

CCSS.HSF.TF.B.7

Solve equation for  $0\le\theta<2\pi$  .
 $2\sqrt{3}\sec\theta\cos\theta=-3\sec\theta$  

•  $\theta=\frac{5\pi}{6}$  

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

•  $\theta=\frac{7\pi}{6},\frac{4\pi}{3}$  

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

Tags

CCSS.HSF.TF.B.7

Solve the equation. Restrict your answer to [0,2π).

 $4+\csc\left(\theta+\frac{\pi}{3}\right)=6$  

•  $\frac{\pi}{2}$  

•  $\frac{11\pi}{6}$  

•  $\frac{4\pi}{3}$  

•  $0$  

• no solution

Tags

CCSS.HSF.TF.B.7

Solve the equation. Restrict your answer to [0,2π).

 $-2\sqrt{2}=4\sin3\theta$  

•  $\left\{\frac{\pi}{24},\frac{13\pi}{24},\frac{7\pi}{12},\frac{25\pi}{24},\frac{29\pi}{24},\frac{5\pi}{4},\frac{7\pi}{4}\right\}$  

•  $\left\{\frac{7\pi}{12},\frac{25\pi}{24},\frac{13\pi}{12},\frac{7\pi}{4},\frac{23\pi}{12}\right\}$  

•  $\left\{\frac{25\pi}{24},\frac{41\pi}{24},\frac{7\pi}{4}\right\}$  

•  $\left\{\frac{5\pi}{12},\frac{7\pi}{12},\frac{13\pi}{12},\frac{5\pi}{4},\frac{7\pi}{4},\frac{23\pi}{12}\right\}$  

Tags

CCSS.HSF.TF.B.7

Solve the equation. Restrict your answer to [0,2π).

 $5\cos^2\theta=-1-3\cos\theta+3\cos^2\theta$  

•  $\frac{2\pi}{3}$  

•  $\pi$  

•  $\frac{4\pi}{3}$  

•  $\frac{5\pi}{3}$  

•  $\frac{\pi}{3}$  

Tags

CCSS.HSF.TF.B.7