Question

Solve the equation on the interval 0 less than or equals theta less than 2 pi 0≤θ<2π. 2 cosine theta plus 1 equals 0 2cosθ+1=0

Answer 1

θ = 2π/3 or 5π/3

Explanation:

2 cosθ + 1= 0

when + 1 goes to R H S Side than it becomes negative by transposition method

2 cos = -1

now by dividing by 2 both sides we get

cosθ = -
`(1)/(2)`

since cosθ is negative

Cosθ = - cos 60°

it means either cosθ lies in 2nd or third quadrant

θ = π - π/3

or

θ = 2π- π/3

so θ = 2π/3 or 5π/3