An equation is given. (Enter your answers as a comma-separated list. Round terms to three decimal places where appropriate. sin 2θ = 3 cos 2θ

Question

(a) Find all solutions of the equation.

(b) Find the solutions in the interval [0, 2π)

Answer 1

A useful number for this problem will be the arctan(3) in the first quadrant. This number is

is approximately 1.249.

The equation can be written as tan(2 θ) = 3. The solution to this equation is θ = (1/2) 1.249 + n π/2

where n is any integer. This can be checked by direct substitution because tan(n π) = 0 for integer n.

The values of n that cause θ to be in the standard interval are n =0, n = 1 , n = 2, n = 3