Respuesta :

Answer:

see explanation

Step-by-step explanation:

Given

2cosΘ - [tex]\sqrt{2}[/tex] = 0 ( add [tex]\sqrt{2}[/tex] to both sides )

2cosΘ = [tex]\sqrt{2}[/tex] ( divide both sides by 2 )

cosΘ = [tex]\frac{\sqrt{2} }{2}[/tex]

Since cosΘ > 0 then Θ is in first and fourth quadrants, hence

Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{\sqrt{2} }{2}[/tex] ) = [tex]\frac{\pi }{4}[/tex]

OR

Θ = 2π - [tex]\frac{\pi }{4}[/tex] = [tex]\frac{7\pi }{4}[/tex]

solutions are Θ = [tex]\frac{\pi }{4}[/tex], [tex]\frac{7\pi }{4}[/tex]

Answer:

π/4, 7π/4.

Step-by-step explanation:

2 cos O - √2 = 0

2 cos O = √2

cos O  = √2/2

This is an angle in  45-45-90 triangle where  the sides are in the ratio

1:1:√2 where the cosine of 45 degrees = 1 /√2 = √2/2.

In radians it is π/4.

The cosine is also positive in the fourth quadrant so the other solution is

7π/4.

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