Question

Determine two unique values of θ in the interval [0,2π), such that sec(θ)=2√3/3

Answer 1

`\sec(\theta )=\cfrac{2√(3)}{3}\implies \sec(\theta )=\cfrac{2√(3)}{√(3)\cdot √(3)}\implies \sec(\theta )=\cfrac{2}{√(3)}\implies \cfrac{1}{\cos(\theta )}=\cfrac{2}{√(3)} \\\\\\ √(3)=2\cos(\theta )\implies \cfrac{√(3)}{2}=\cos(\theta )\implies \cos^(-1)\left( \cfrac{√(3)}{2} \right)=\theta \implies \theta = \begin{cases} (\pi )/(6)\\\\ (11\pi )/(6) \end{cases}`