Question

PLEASE ANSWER ASAP

Answer 1

The relationship is that cos 7pi/6 and cos 5pi/6 both are cosines of angles that have a reference angle of pi/6. cos 7pi/6 = cos 5pi/6 = -√3/2

Answer 2

It is known
 $\dfrac{\pi}{6} =30^{\circ}$ and 
 $\cos \dfrac{\pi}{6}= \dfrac{ \sqrt{3} }{2}$ (if you want to determine cosine of 30° you should draw the perpendicular line to the x-axis and find the point of intersection, the value of x-coordinate is the cosine of 30°).

The angle $\dfrac{5\pi}{6} =150^{\circ}$ and
$\cos \dfrac{5\pi}{6}=- \dfrac{ \sqrt{3} }{2}$ (see image).
The angle $\dfrac{7\pi}{6} =210^{\circ}$ and

$\cos \dfrac{7\pi}{6}=- \dfrac{ \sqrt{3} }{2}$ (see image).