Solve the trigonometric equation in the interval [0, 2π). Give the exact value, if possible; otherwise, round your answer to two decimal places. (Enter your answers as a comma-separated list.) sin(2θ) − cos(θ) = 0

Accepted Solution

Answer:θ∈{[tex]\frac{\pi }{8},\frac{5\pi }{8},\frac{9\pi }{8},\frac{13\pi }{8}[/tex]}Explanation:The given equation is [tex]sin(2\theta )-cos(2\theta )=0[/tex][tex]\Rightarrow sin(2\theta )=cos(2\theta )\\\\\therefore \frac{sin(2\theta )}{cos(2\theta )}=1\\\\tan(2\theta )=1\\\\\therefore 2\theta =n\pi +\frac{\pi}{4}\\\\\therefore \theta =\frac{n\pi }{2}+\frac{\pi }{8}[/tex]Applying values on 'n' we obtain values of θ that beling to [0,2π)For n=0, θ=[tex]\frac{\pi }{8}[/tex]For n=1, θ =[tex]\frac{5\pi }{8}[/tex]For n=2,θ =[tex]\frac{9\pi }{8}[/tex]For n=3,θ =[tex]\frac{13\pi }{8}[/tex]