Respuesta :
It is known
[tex]\dfrac{\pi}{6} =30^{\circ}[/tex] and
[tex]\cos \dfrac{\pi}{6}= \dfrac{ \sqrt{3} }{2} [/tex] (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 [tex]\dfrac{5\pi}{6} =150^{\circ}[/tex] and
[tex]\cos \dfrac{5\pi}{6}=- \dfrac{ \sqrt{3} }{2} [/tex] (see image).
The angle [tex]\dfrac{7\pi}{6} =210^{\circ}[/tex] and
[tex]\cos \dfrac{7\pi}{6}=- \dfrac{ \sqrt{3} }{2} [/tex] (see image).
[tex]\dfrac{\pi}{6} =30^{\circ}[/tex] and
[tex]\cos \dfrac{\pi}{6}= \dfrac{ \sqrt{3} }{2} [/tex] (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 [tex]\dfrac{5\pi}{6} =150^{\circ}[/tex] and
[tex]\cos \dfrac{5\pi}{6}=- \dfrac{ \sqrt{3} }{2} [/tex] (see image).
The angle [tex]\dfrac{7\pi}{6} =210^{\circ}[/tex] and
[tex]\cos \dfrac{7\pi}{6}=- \dfrac{ \sqrt{3} }{2} [/tex] (see image).

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