Answer: 30° and 330°
Step-by-step explanation:
sec θ = [tex]\frac{2\sqrt{3}}{3}[/tex]
sec θ = [tex]\frac{1}{cos(\theta)}[/tex]
[tex]\frac{1}{cos(\theta)}[/tex] = [tex]\frac{2\sqrt{3}}{3}[/tex]
cos θ = [tex]\frac{3}{2\sqrt{3}}[/tex]
cos θ = [tex]\frac{3}{2\sqrt{3}}(\frac{\sqrt{3}}{\sqrt{3}})[/tex]
cos θ = [tex]\frac{3\sqrt{3}}{3*2}[/tex]
cos θ = [tex]\frac{\sqrt{3}}{2}[/tex]
Look at the Unit Circle to see that cos = [tex]\frac{\sqrt{3}}{2}[/tex] at 30° and 330° ( which is equivalent to π/6 and 11π/6)
