Question

I need help breaking this down

Answer 1

π/4, 7π/4.

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.

Answer 2

see explanation

Explanation:

Given

2cosΘ -
`√(2)` = 0 ( add
`√(2)` to both sides )

2cosΘ =
`√(2)` ( divide both sides by 2 )

cosΘ =
`(√(2) )/(2)`

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

Θ =
`cos^(-1)` (
`(√(2) )/(2)` ) =
`(\pi )/(4)`

OR

Θ = 2π -
`(\pi )/(4)` =
`(7\pi )/(4)`

solutions are Θ =
`(\pi )/(4)`,
`(7\pi )/(4)`