Answer:
[tex]\theta_{1} \approx 30.473^{\textdegree}[/tex]
[tex]\theta_{2} \approx 120.473^{\textdegree}[/tex]
[tex]\theta_{3} \approx 210.473^{\textdegree}[/tex]
[tex]\theta_{4}\approx 300.473^{\textdegree}[/tex]
Step-by-step explanation:
The equation needs to be rearranged in terms of one trigonometric function:
[tex]5\cdot \sin 2\theta - 9\cdot \cos 2\theta = 0[/tex]
[tex]5\cdot \tan 2\theta - 9 = 0[/tex]
[tex]5\cdot \tan 2\theta = 9[/tex]
[tex]\tan 2\theta = \frac{9}{5}[/tex]
[tex]\theta = \frac{1}{2}\cdot \tan^{-1} \left(\frac{9}{5} \right)[/tex]
The tangent function has positive values in the 1st and 3rd Quadrants. Then, the solutions are:
[tex]\theta_{1} \approx 30.473^{\textdegree}[/tex]
[tex]\theta_{2} \approx 120.473^{\textdegree}[/tex]
[tex]\theta_{3} \approx 210.473^{\textdegree}[/tex]
[tex]\theta_{4}\approx 300.473^{\textdegree}[/tex]
