An equation is given.

Question

sin(2θ)=4cos(2θ)

(a). Find all solutions of the equation. θ=?

(b). Find the solutions in the interval [0, 2 pi ). θ=?

Answer 1

sin2x = 4cos2x

sin2x/cos2x = 4

tan2x = 4

2x = about 76 degrees (use a calculator with an inverse tangent function) or 180+76 = 256 degrees

x = about 76/2 = 38 degrees or 256/2 = 128 degrees

ad 360n to each solution where n = any integer

x = 38 + 360n or 128 + 360n degrees

solutions are all in the 1st or 2nd quadrants