Solve equations of the form cos(x)=a - High school Trigonometry Exercises

Solve the following equations.

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

x = \left(\dfrac{5\pi}{6}\right)+2n\pi, n \in \mathbb{Z} or x = \left(\dfrac{7\pi}{6}\right)+2n\pi, n \in \mathbb{Z}

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

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

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

\cos\left(x\right) = 0

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

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

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

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

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

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

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

\cos\left(x\right) = 1

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

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

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

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

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

x = \left(\dfrac{\pi}{4}\right)+2n\pi, \ n \in \mathbb{Z} or x = \left(\dfrac{7\pi}{4}\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}{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{5\pi}{3}\right)+2n\pi, \ n \in \mathbb{Z}

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

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

x = \pi\left(2n + 1\right), 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 = \dfrac{3\pi}{2}\left(4n + 1\right)

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

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{\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{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}{3}\right)+2n\pi, \ n \in \mathbb{Z}