Answer :
It is given that:
[tex]\angle\theta=\frac{11\pi}{6}[/tex]This can be written as:
[tex]\frac{11\pi}{6}=11\times\frac{\pi}{6}[/tex]Thus, the reference angle (the acute angle between terminal side and x-axis of the angle) is pi/6
We know pi radians = 180 degrees, thus,
[tex]\frac{\pi}{6}=\frac{180}{6}=30\degree[/tex]The first two statements are not correct.
Now, we have to find the respective values of sin, cos, and tan (THETA). First,
[tex]\frac{11\pi}{6}=\frac{11(180)}{6}=330\degree[/tex]This angle falls in the 4th quadrant. The reference angle is 30 degrees.
Let's find the values of sin, cos, and tan of theta.
[tex]\cos \theta=\cos \frac{11\pi}{6}=\cos \frac{\pi}{6}=\frac{\sqrt[]{3}}{2}[/tex]then,
[tex]\sin \theta=\sin \frac{11\pi}{6}=-\sin \frac{\pi}{6}=-\frac{1}{2}[/tex]Note that the value of sine is negative in the fourth quadrant.
Then,
[tex]\tan \theta=\tan \frac{11\pi}{6}=-\tan \frac{\pi}{6}=-\frac{1}{\sqrt[]{3}}[/tex]Thus, the statements that are true are bolded below:
the measure of the reference angle is 45°
the measure of the reference angle is 60°
cos(0)= square root 3 /2
sin(0)= 1/2
tan(0)=1
the measure of the reference angle is 30°
