Solving Trig Basic Trig Equations

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

• 0
• No solution
• π
• 3π/2

Solve on the domain [0, 2π)
4sin²x = 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 on the domain [0, 2π)
cos x + 2 = 3 cos x

• 0, 2π/3, 4π/3
• π
• 0
• No solution

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

• 0
• No solution
• π
• 3π/2

Which of the following is NOT
a solution to
 $\sin x=\frac{\sqrt{3}}{2}$  ?

•  $\frac{\pi}{3}$  

•  $\frac{2\pi}{3}$  

•  $\frac{7\pi}{3}$  

•  $\frac{5\pi}{3}$  

                Solve  $\sin x=-1$                        
on the interval  $\left[0,2\pi\right)$  

•   $x=\frac{\pi}{2\ },\ \frac{3\pi}{2}$  

•  $x=\frac{\pi}{2}$  

•  $x=\frac{3\pi}{2}$  

•  $x=\pi$  

One solution of tan x = -1 is 135⁰, which of these is another solution?

• 315⁰
• 135⁰
• 225⁰
• 330⁰

What is a good first step to solving this equation?

 $5\cos x-\sqrt{3}=3\cos x$  

•  Divide everything by 5

•  Subtract  $3\cos x$  from both sides of the equation

• Divide everything by 3

• Add  $3\cos x$  to both sides of the equation

What is a good next step to solving this equation?

 $2\cos x-\sqrt{3}=0$  

•  Subtract  $\sqrt{3}$  from both sides of the equation

•  Add  $\sqrt{3}$  to both sides of the equation
  
  

• Divide both sides of the equation by  $\cos x$  

• Stop because there is no solution

Check all solutions to this equation
 $\cos x=\frac{\sqrt{3}}{2}$   

•   $\frac{\pi}{6}+2n\pi$  

•  
   $\frac{\pi}{3}+2n\pi$  
  

•  $\frac{11\pi}{6}+2n\pi$  

•  $\frac{2\pi}{3}+2n\pi$