Solve the equation (x in radians and $$\boldsymbol { \theta }$$ 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.
-$$\sin ^ { 2 } x + \sin x = 0$$

Question

Quizplus · Accepted Answer

To solve the equation $\sin^2 x + \sin x = 0$, factor it to get $\sin x(\sin x + 1) = 0$. This gives two equations: $\sin x = 0$ and $\sin x = -1$. The solutions to $\sin x = 0$ are $x = n\pi$, where $n$ is any integer, because sine is zero at integer multiples of $\pi$. The solution to $\sin x = -1$ is $x = \frac{3\pi}{2} + 2n\pi$, because sine is -1 at an angle of $\frac{3\pi}{2}$ plus any integer multiple of $2\pi$. Therefore, the correct set of solutions is $\left\{ n\pi, \frac{3\pi}{2} + 2n\pi \right\}$.

Solve the Equation (X in Radians And θ\boldsymbol { \theta }θ

Solve the Equation (X in Radians And $\boldsymbol { \theta }$