Solve the equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth.
-$\frac { 4 \tan \theta } { 21 - \tan ^ { 2 } \theta } = 1$

Question

Quizplus · Accepted Answer

Given the equation $\frac { 4 \tan \theta } { 21 - \tan ^ { 2 } \theta } = 1$, we can solve for $\tan \theta$ by cross-multiplying and solving the resulting quadratic equation. The solutions to this equation will repeat every 180 degrees because the tangent function has a period of 180 degrees. The given solutions $71.6^\circ$ and $98.1^\circ$ are specific solutions within one period, and adding $180^\circ n$ accounts for the periodic nature of the tangent function, where $n$ is an integer.

Solve the Equation (X in Radians and θ in Degrees) 4tan⁡θ21−tan⁡2θ=1\frac { 4 \tan \theta } { 21 - \tan ^ { 2 } \theta } = 121−tan2θ4tanθ​=1

Solve the Equation (X in Radians and θ in Degrees) $\frac { 4 \tan \theta } { 21 - \tan ^ { 2 } \theta } = 1$