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

`\theta_(1) \approx 30.473^(\textdegree)`

`\theta_(2) \approx 120.473^(\textdegree)`

`\theta_(3) \approx 210.473^(\textdegree)`

`\theta_(4)\approx 300.473^(\textdegree)`

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 = (9)/(5)`

`\theta = (1)/(2)\cdot \tan^(-1) \left((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)`