Solve the equation on the interval [0,2 pie)

Question

4 cos^2 x=1

x= ? Type an exact answer use integers of fractions for any number in the expression

Answer 1

Hi Aireeyon,

4 cos^2 x=1 both side s divided by 4

cos^(x) = 1/4 take a root of both sides

cos(x) = ±1/2

cos(x) = 1/2 -----> x = Π/3 and 2Π - Π/3 = 5Π/3

cos(x) = -1/2 ----> x = 2Π/3 and 2Π- 2Π/3 = 4Π/3

As a result all answers between 0 , 2Π are { Π/3, 2Π/3, 4Π/3, 5Π/3}

I hope it is useful,

Minoo