Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.
-$\tan ^ { 2 } 2 \theta = 5$
A) $\left\{ 33 ^ { \circ } , 57 ^ { \circ } , 123 ^ { \circ } , 147 ^ { \circ } , 213 ^ { \circ } , 237 ^ { \circ } , 303 ^ { \circ } , 327 ^ { \circ } \right\}$
B) $\left\{ 0 ^ { \circ } \right\}$
C) $\left\{ 0 ^ { \circ } , 45 ^ { \circ } , 90 ^ { \circ } , 135 ^ { \circ } , 180 ^ { \circ } , 225 ^ { \circ } , 270 ^ { \circ } \right\}$
D) $\left\{ 0 ^ { \circ } , 90 ^ { \circ } , 180 ^ { \circ } , 270 ^ { \circ } \right\}$

Question

Quizplus · Accepted Answer

First, solve $\tan^2 2\theta = 5$ by taking the square root, giving $\tan 2\theta = \pm \sqrt{5}$. Solving for $2\theta$ gives angles that, when divided by 2, result in the solutions listed in option A. These solutions are found by considering the periodicity of the tangent function and the specified interval.

Solve the Equation for Solutions in the Interval [0°, 360°) tan⁡22θ=5\tan ^ { 2 } 2 \theta = 5tan22θ=5

Solve the Equation for Solutions in the Interval [0°, 360°) $\tan ^ { 2 } 2 \theta = 5$