Question

What is cos3phi= 1/2??? Please help and explain!

Answer 1

`\large\boxed{\Phi=(\pi)/(9)+(2k\pi)/(3)\ or\ \Phi=-(\pi)/(9)+(2k\pi)/(3)}`

Explanation:

`\cos3\Phi=(1)/(2)\qquad\text{substitute}\ 3\Phi=\theta\\\\\cos\theta=(1)/(2)\iff\theta=(\pi)/(3)+2k\pi\ or\ \theta=-(\pi)/(3)+2k\pi\qquad k\in\mathbb{Z}\\\\\text{We're going back to substitution:}\\\\3\Phi=(\pi)/(3)+2k\pi\ or\ 3\Phi=-(\pi)/(3)+2k\pi\qquad\text{divide both sides by 3}\\\\\Phi=(\pi)/(9)+(2k\pi)/(3)\ or\ \Phi=-(\pi)/(9)+(2k\pi)/(3)`