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.
-$4 \sin ^ { 2 } x - 1 = 0$

Question

Quizplus · Accepted Answer

First, solve the equation $4 \sin ^ { 2 } x - 1 = 0$. This simplifies to $\sin ^ { 2 } x = \frac{1}{4}$, which means $\sin x = \pm \frac{1}{2}$. The solutions for $\sin x = \frac{1}{2}$ are $x = \frac{\pi}{6} + 2n\pi$ and $x = \frac{5\pi}{6} + 2n\pi$, where $n$ is an integer. However, since the sine function has a period of $\pi$, we include all solutions within that period by adjusting the general solution to $x = \frac{\pi}{6} + n\pi$ and $x = \frac{5\pi}{6} + n\pi$, which matches option B.

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

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