Solving Trig Equations

Solve equation on $0\le\theta<2\pi$ 

 $-2+\cot\theta=-3$  

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

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

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

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

Tags

CCSS.HSF.TF.B.7

Solve equation on $0\le\theta<2\pi$  .

 $1=5-8\cos\theta$  

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

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

•  $\theta=\frac{\pi}{6}$  

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

Tags

CCSS.HSF.TF.B.7

Solve equation on $0\le\theta<2\pi$  .

 $4+4\tan\theta=0$  

•  $\theta=\pi$  

•  $\theta=\frac{7\pi}{4}$  

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

•  $\theta=0,\frac{3\pi}{4}$  

Tags

CCSS.HSF.TF.B.7

Solve equation on $0\le\theta<2\pi$  .

 $1=5-8\cos\theta$  

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

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

•  $\theta=\frac{\pi}{6}$  

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

Tags

CCSS.HSF.TF.B.7

Solve on  [0, 2π)

 $4\sin^2x=3$   

• 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.HSF.TF.B.7

Solve equation on $0\le\theta<2\pi$  .

 $3\sin^2\theta+4=5+\sin^2\theta$  

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

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

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

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

Tags

CCSS.HSF.TF.B.7

Solve on the interval  $\left[0,2\pi\right)$  

 $2\cos^2x-3\cos\left(x\right)+1=0$ 

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

•  $x=\frac{\pi}{6},\frac{\pi}{2},\frac{11}{6}$  

•  $x=0,\pi,2\pi$  

•  $x=\frac{\pi}{6},\frac{\pi}{2},\frac{5\pi}{6}$  

Tags

CCSS.HSF.TF.B.7

Solve on [0,2π]

 $4\cos^2x-4\cos x+1=0$  

• $\frac{\pi}{6}\ and\ \frac{11\pi}{6}$

• $\frac{\pi}{3}\ and\ \frac{5\pi}{3}$

• no solution

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

Tags

CCSS.HSF.TF.B.7

 $4\cos x\ -\ 3\ =\ 2\cos x$  

Describe the equation below.

• a linear equation

• a quadratic equation with no linear term

• a quadratic equation with no constant term

• a quadratic trinomial

Tags

CCSS.HSA.REI.C.7

Describe the equation below:

 $2\cos x-3\cos^2x\ =\ 4$ 

• a linear equation

• a quadratic equation with no linear term

• a quadratic equation with no constant term

• a quadratic trinomial

Tags

CCSS.HSA.REI.C.7