Solve Trig Equations Review

Why doesn't 2cosx − 3 = 0 have solutions?

• cos x is never bigger than one

• cos x is never equal to a fraction

• Actually, this equation does have a solution, x = π

• This equation will have a solution tomorrow.

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  $0\le\theta<2\pi$  .
 $-3=\cot^2\theta-6$  

•  $\theta=\frac{\pi}{6},\frac{7\pi}{4},\frac{11\pi}{6}$  

•  $\theta=\frac{7\pi}{6},\frac{5\pi}{4},\frac{11\pi}{6}$  

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

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

Tags

CCSS.HSF.TF.B.7

Solve equation for  $0\le\theta<2\pi$  .
 $4+\csc^2\theta=2\csc^2\theta$  

•  $\theta=\frac{5\pi}{6},\frac{4\pi}{3}$  

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

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

•  $\theta=\frac{\pi}{6}$  

Tags

CCSS.HSF.TF.B.7

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

•  $\theta=\frac{5\pi}{4},\frac{11\pi}{6}$  

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

•  $\theta=0,\pi,\frac{5\pi}{4},\frac{7\pi}{4}$  

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

Tags

CCSS.HSF.TF.B.7

Solve equation for  $0\le\theta<2\pi$  .
 $3\sin^2\theta=7\sin^2\theta+4\sin\theta+1$  

•  $\theta=\frac{7\pi}{6}$  

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

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

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

Tags

CCSS.HSF.TF.B.7

 $Solve\ \ \ 3\sec^2x\ =\ 4\ \ for\ \ 0\ \le\ x\ <\ 2\pi$  

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

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

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

•  $0,\ \frac{\pi}{2},\ \pi,\ \frac{3\pi}{2}$  

Tags

CCSS.HSF.TF.B.7

Solve: 2cos(2x)= -√2

• $\frac{3\pi}{8},\frac{5\pi}{8},\frac{11\pi}{8},\frac{13\pi}{8}$
  

• $\frac{3\pi}{4},\frac{5\pi}{4}$
  

• $\frac{\pi}{8},\frac{7\pi}{8},\frac{9\pi}{8},\frac{15\pi}{8}$
  

• $\frac{\pi}{4},\frac{7\pi}{4}$
  

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