Question

I need help breaking this down

Answer 1

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.

Answer 2

Answer:

see explanation

Step-by-step explanation:

Given

2cosΘ - $\sqrt{2}$ = 0 ( add $\sqrt{2}$ to both sides )

2cosΘ = $\sqrt{2}$ ( divide both sides by 2 )

cosΘ = $\frac{\sqrt{2} }{2}$

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

Θ = $cos^{-1}$ ( $\frac{\sqrt{2} }{2}$ ) = $\frac{\pi }{4}$

OR

Θ = 2π - $\frac{\pi }{4}$ = $\frac{7\pi }{4}$

solutions are Θ = $\frac{\pi }{4}$, $\frac{7\pi }{4}$