SOLUTION: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. (-2/sqrt 3)cos 3θ = 1 a.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. (-2/sqrt 3)cos 3θ = 1 a.      Log On


   

Question 1009674: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate.
(-2/sqrt 3)cos 3θ = 1
a.)find all the solution of the equations.
b.)find the solutions in the interval [0,2pi)

Please help so confused??
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
%28-2%2Fsqrt%283%29%29%2Acos%283%2Atheta%29 = 1.

After multiplying both sides by -sqrt%283%29%2F2 this equation is equivalent to this one:

cos%283%2Atheta%29 = -sqrt%283%29%2F2.

The general solution of the last equation is 

3%2Atheta = +/- 5pi%2F6 + 2%2Ak%2Api, k = 0, +/-1, +/-2, . . . 

Hence, 

theta = +/- 5pi%2F18 + %282%2F3%29%2Ak%2Api, k = 0, +/-1, +/-2, . . . 

is the general solution to the original equation.

Regarding the interval [0, 2pi), the solutions for theta are 

theta = 5pi%2F18, 7pi%2F18, 5pi%2F18 + %282%2F3%29%2Api, 7pi%2F18 + %282%2F3%29%2Api, 5pi%2F18 + %284%2F3%29%2Api and 7pi%2F18 + %284%2F3%29%2Api.