Question

Find all degree solutions in the interval 0° ≤ θ < 360°. If rounding is necessary, round to the nearest tenth of a degree. Use your graphing calculator to verify the solution graphically. (Enter your answers as a comma-separated list.) 5 sin2 θ − 9 cos 2θ = 03

Answer 1

Answer:

$\theta_{1} \approx 30.473^{\textdegree}$

$\theta_{2} \approx 120.473^{\textdegree}$

$\theta_{3} \approx 210.473^{\textdegree}$

$\theta_{4}\approx 300.473^{\textdegree}$

Step-by-step explanation:

The equation needs to be rearranged in terms of one trigonometric function:

$5\cdot \sin 2\theta - 9\cdot \cos 2\theta = 0$

$5\cdot \tan 2\theta - 9 = 0$

$5\cdot \tan 2\theta = 9$

$\tan 2\theta = \frac{9}{5}$

$\theta = \frac{1}{2}\cdot \tan^{-1} \left(\frac{9}{5} \right)$

The tangent function has positive values in the 1st and 3rd Quadrants. Then, the solutions are:

$\theta_{1} \approx 30.473^{\textdegree}$

$\theta_{2} \approx 120.473^{\textdegree}$

$\theta_{3} \approx 210.473^{\textdegree}$

$\theta_{4}\approx 300.473^{\textdegree}$