5.4 Practice: Solving Trig Equations

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

•  $\theta=\pi$  

•  $\theta=\frac{7\pi}{4}$  

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

•  $\theta=0,\frac{3\pi}{4}$  

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

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

•  $\theta=\frac{\pi}{3}$  

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

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

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

 $3\cot x+5=5$  

•  $\frac{\pi}{2},\ \frac{3\pi}{2}$  

•  $0,\ \pi$  

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

•  $\frac{\pi}{4},\ \frac{5\pi}{4}$  

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

 $2\cos^2x-1=1$  

•  $0,\ \pi$  

•  $\frac{\pi}{2},\ \frac{3\pi}{2}$  

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

• No solution

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

 $4\sin^2x=3$  

• π/6, 11π/6

• π/3, 2π/3

• π/6, 5π/6, 7π/6, 11π/6

• π/3, 2π/3, 4π/3, 5π/3

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

 $3\sec^2x=4$  

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

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

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

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

Solve equation for  $0\le\theta<2\pi$  .
 $\cos x\tan x+\cos x=0$  

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

•  $0,\ \frac{3\pi}{4},\ \pi,\ \frac{7\pi}{4}$  

•  $\frac{\pi}{2},\ \frac{3\pi}{4},\ \frac{3\pi}{2},\ \frac{7\pi}{4}$  

•  $0,\ \frac{\pi}{4},\ \pi,\ \frac{5\pi}{4}$  

To solve this equation, cos²x + sinx = 1, replace cos²x with

• 1/(sec²x)

• sin²x − 1

• 1 − sin²x

• 1 + tan²x

Tags

CCSS.HSF.TF.C.8