Question

PLEASE HELP (100 POINTS)

Answer 1

θ = π/3 and 5π/3

Explanation:

f(x) = 2cos²θ

g(x) = -1 + 4cosθ - 2cos²θ

Since they intersect,

2cos²θ = -1 + 4cosθ + 2cos²θ

4cos²θ - 4cosθ + 1 = 0

(2cosθ - 1)² = 0

cosθ = 1/2

cosθ = π/3

At (0, 2π) interval,

θ = π/3 and 2π - π/3 = 5π/3

The correct option is the last one.

Answer 2

Option B

Explanation:

• put π/3 first

`\\ \rm\Rrightarrow f(\pi/3)`

`\\ \rm\Rrightarrow 2cos^2(\pi /3)=2(1/4)=1/2`

`\\ \rm\Rrightarrow g(\pi/3)`

`\\ \rm\Rrightarrow -1+4cos(\pi/3)-2cos^2(\pi/3)=-1+2-1/2=1/2`

• Yes verified

Now other one is

`\\ \rm\Rrightarrow cos(2\pi -\pi/3)`

`\\ \rm\Rrightarrow cos(6\pi-\pi/3)`

`\\ \rm\Rrightarrow cos(5\pi/3)`

Option B is correct