Solve equations of the form sin(x)=a - High school Algebra II Exercises

Solve the following equations.

\sin\left(x\right) = \dfrac{-1}{2}

x = \left(\dfrac{7\pi}{6}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{11\pi}{6}\right)+2n\pi, \ n \in \mathbb{Z}

x = \left(\dfrac{\pi}{6}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{5\pi}{6}\right)+2n\pi, \ n \in \mathbb{Z}

x = \left(\dfrac{\pi}{2}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{3\pi}{2}\right)+2n\pi, \ n \in \mathbb{Z}

x = \left(\dfrac{4\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{7\pi}{6}\right)+2n\pi, \ n \in \mathbb{Z}

\sin\left(x\right) = \dfrac{-\sqrt{2}}{2}

x = \left(\dfrac{5\pi}{4}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{7\pi}{4}\right)+2n\pi, \ n \in \mathbb{Z}

x = \dfrac{\pi}{2}\left(2n + 1\right), n \in \mathbb{Z}\\

x = \left(\dfrac{3\pi}{4}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{5\pi}{4}\right)+2n\pi, \ n \in \mathbb{Z}

x = \left(\dfrac{\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{2\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z}

\sin\left(x\right) = \dfrac{-\sqrt{3}}{2}

x = \left(\dfrac{4\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{5\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z}

x = \left(\dfrac{2\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{5\pi}{6}\right)+2n\pi, \ n \in \mathbb{Z}

x = \left(\dfrac{7\pi}{6}\right)+2n\pi, n \in \mathbb{Z} or x = \left(\dfrac{11\pi}{6}\right)+2n\pi, n \in \mathbb{Z}

x = \left(\dfrac{\pi}{6}\right)+2n\pi, n \in \mathbb{Z} or x = \left(\dfrac{5\pi}{6}\right)+2n\pi, n \in \mathbb{Z}

\sin\left(2x\right) = -1

x = \left(\dfrac{3\pi}{4}\right)+n\pi, \ n \in \mathbb{Z}

x = \left(\dfrac{3\pi}{2}\right)+2n\pi, \ n \in \mathbb{Z}

x = \pi\left(n + \dfrac{1}{2}\right), n \in \mathbb{Z}

x = \dfrac{\pi}{2}\left(n + \dfrac{3}{2}\right), n \in \mathbb{Z}

\sin\left(2x\right) = \dfrac{-1}{2}

x = \left(\dfrac{7\pi}{12}\right) + \pi n, n \in \mathbb{Z} or x = \left(\dfrac{11\pi}{12}\right) + \pi n, n \in \mathbb{Z}

x = \left(\dfrac{7\pi}{6}\right) + 2\pi n, n \in \mathbb{Z}\\ or x = \left(\dfrac{11\pi}{6}\right) + 2\pi n, n \in \mathbb{Z}

x = \left(\dfrac{7\pi}{12}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{11\pi}{12}\right)+2n\pi, \ n \in \mathbb{Z}

x = \left(\dfrac{5\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{7\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z}

\sin\left(x\right) = 0

x = \pi n, \ n \in \mathbb{Z}

x = \dfrac{\pi}{2}\left(2n+1\right), \ n \in \mathbb{Z}

x = 2\pi n, \ n \in \mathbb{Z}

x = \dfrac{\pi}{2}\left(4n + 1\right), \ n \in \mathbb{Z}

\sin\left(x\right) = \dfrac{\sqrt{3}}{2}

x = \left(\dfrac{\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{2\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z}

x = \left(\dfrac{\pi}{6}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{5\pi}{6}\right)+2n\pi, \ n \in \mathbb{Z}

x = \left(\dfrac{2\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{4\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z}

x = \left(\dfrac{4\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{7\pi}{6}\right)+2n\pi, \ n \in \mathbb{Z}