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Find all solutions of the equation in the interval [0, 2 π).
2cos θ - √ 2 = 0
Write your answer in radians in terms of π. If there is more than one solution, separate them with commas.

Sagot :

Polyblock

Answer:

θ = [tex]\frac{\pi}{4}[/tex]  

θ = [tex]\frac{7\pi}{4}[/tex]

Step-by-step explanation:

2cosθ - √2 = 0

First, add √ 2 to both sides

2cosθ - √2 = 0

          +√2  +√2

2cosθ = √2

Divide both sides by 2

2cosθ/2 = √2 / 2

cosθ = [tex]\frac{2}{\sqrt{2}}[/tex]

Use arccos to find θ

arccos([tex]\frac{2}{\sqrt{2}}[/tex]) = [tex]\frac{\pi}{4}[/tex]  and  [tex]\frac{7\pi}{4}[/tex] = θ

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