Question

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. If there is no solution, enter NO SOLUTION.) 2 cos(3θ) = 1 (a) Find all solutions of the equation. (b) Find the solutions in the interval [0, 2π).

Answer 1

Explanation:

Given that a trignometric equation is as follows

`2cos(3t) =1\\`

Divide by 2

`cos(3t) =0.5\\`

b) 3t would be either in I quadrant or IV quadrant in the interval [0, 2π).

`3t=(\pi)/(3) ,2\pi- (\pi)/(3) \\t =(\pi)/(9) , \frac{5\pi}9}`

a) To find general solution

General solution is

±
`2k\pi`±
`(\pi)/(3)`