10.5 Solving Trig Equations

How many solutions does the following equation have on the given interval?

 $\sin x=\frac{1}{2}$  when  $0\le x<2\pi$  

• 0

• 1

• 2

• 4

How many solutions does the following equation have on the given interval?

 $\tan^2x=3$  when  $0\le x<2\pi$  

• 0

• 1

• 2

• 4

 $\cos x+\cos^2x=0$  

What method would you use to solve the equation?

• greatest common factor

• cancel cosines

• combine like terms

• square roots

Solve $\cos x+\cos^2x=0$  on the interval  $\pi\le x<\frac{3\pi}{2}$  

•  $\frac{\pi}{2}$  
  

•  $\frac{3\pi}{2}$ 

•  $\pi$  
  

•  $\frac{5\pi}{4}$  
  

 $\cot^2x-2\cot x+1=0$  

What method would you use to solve the equation?

• square roots

• combining like terms

• factoring

• trig identities

 $\cot^2x-2\cot x+1=0$  

Solve on the interval  $\pi\le x<2\pi$  

•  $\frac{\pi}{4}$  
  

•  $\frac{3\pi}{4}$  
  

•  $\frac{5\pi}{4}$  
  

•  $\frac{7\pi}{4}$  
  

 $2\sin^2x=2$  

What method would you use to solve the equation?

• square roots

• combining like terms

• factoring

• trig identities

 $2\sin^2x=2$  

Solve the equation on the interval  $0\le x<2\pi$  

• 0

•  $\frac{\pi}{6}$  
  

•  $\frac{\pi}{2}$  
  

•  $\frac{3\pi}{2}$  
  

•  $\pi$  

 $2\sin x\cos x=0$  

What method would you use to solve the equation?

• square roots

• combining like terms

• factoring

• trig identities

 $2\sin x\cos x=0$  

Solve the equation on the given interval  $x\in\left\{all\ real\ numbers\right\}$  

•  $0+\frac{\pi}{2}n$  

•  $0+\pi n$  
  

•  $\frac{\pi}{2}+2\pi n$  
  

•  $0+2\pi n$