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.
-$$\cos ^ { 2 } x - \cos x = 0$$

Question

Quizplus · Accepted Answer

To solve the equation $\cos^2 x - \cos x = 0$, factor it to get $\cos x(\cos x - 1) = 0$. This gives two equations: $\cos x = 0$ and $\cos x = 1$. The solutions to $\cos x = 0$ are $x = \frac{\pi}{2} + n\pi$, and the solutions to $\cos x = 1$ are $x = 2n\pi$, where $n$ is any integer. Combining these gives the set of all solutions as $\left\{ 2n\pi, \frac{\pi}{2} + n\pi \right\}$.

Solve the Equation (X in Radians and θ in Degrees) cos⁡2x−cos⁡x=0\cos ^ { 2 } x - \cos x = 0cos2x−cosx=0

Solve the Equation (X in Radians and θ in Degrees) $\cos ^ { 2 } x - \cos x = 0$