Answer:
- The measure of reference angle is [tex]30^{\circ}[/tex].
- [tex]\cos \theta=\frac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
Converting [tex]\theta[/tex] to degrees,
[tex]\theta=\left(\frac{11\pi}{6} \right) \left(\frac{180}{\pi} \right)=330^{\circ}[/tex]
This means [tex]\theta[/tex] lies in Quadrant 4, and thus its reference angle is [tex]360^{\circ}-330^{\circ}=\boxed{30^{\circ}}[/tex]
Since [tex]\theta[/tex] lies in the fourth quadrant, [tex]\sin \theta[/tex] and [tex]\tan \theta[/tex] are negative.
Since [tex]\theta[/tex] lies in the fourth quadrant, [tex]\cos \theta[/tex] is positive, and is equal to [tex]\cos (30^{\circ})=\boxed{\frac{\sqrt{3}}{2}}[/tex]
