Solving Trig Equations Review

2 sinx+3=2

• π/6,2π/3

• 7π/6

• 7π/6, 11π/6

Solve   $\frac{1}{2}\sec x-1=0$  

• π/6, 5π/6

• π/3, 5π/3

• 2π/3, 4π/3

• 7π/6, 11π/6

Solve 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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4

Which of these is equivalent to 2cos²x − 3cosx = 0 ?

• -cos²x = 0

• cosx(2cosx + 3) = 0

• cosx(2cosx − 3) = 0

• cos x = ⅔

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

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.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve tanx+1=2 on [0, 2π)

• 0 and π

• 3π/4 and 7π/4

• π/4 and 5π/4

• 3π/4 and 5π/4

Solve $2\cos x-4=0$ for all values. 

• No solution

• x = π/3 +2πn, 5π/3 +2πn

• x = π/6 +2πn, 11π/6 +2πn

• x = 2π/3 +2πn, 4π/3 +2πn

Solve  $2\cos^2x-1=0$  for all values

•  $x=\frac{\pi}{4}+2\pi n,\ \ \frac{7\pi}{4}+2\pi n$  

•  $x=\frac{\pi}{4}+2\pi n,\ \frac{3\pi}{4}+2\pi n$  

•  $x=\frac{3\pi}{4}+2\pi n,\ \frac{5\pi}{4}+2\pi n$  sd

•  $x=\frac{\pi}{4}+2\pi n,\ \ \frac{3\pi}{4}+2\pi n,\ \frac{5\pi}{4}+2\pi n,\ \frac{7\pi}{4}+2\pi n$  

Solve equation for  $0\le x<2\pi$  .
 $-2+\cot x=-3$  

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

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

•  $x=\frac{\pi}{3},\frac{4\pi}{3}$  

•  $x=\frac{3\pi}{4},\frac{4\pi}{3}$