Question 853151

I will solve A.

Replace x in g(x) with the given trig values and then use the unit circle diagram to find the exact values. Remember that on the unit circle, the point is (cosine, sine). 

g(5pi/6+pi/6) = g(5pi/6)+g(pi/6) 

cos(5pi/6) + cos(pi/6)

cos(5pi/6) = -sqrt(3)/2

cos(pi/6) = sqrt(3)/2

This means that when added, 

cos(5pi/6) + cos(pi/6 = 

-sqrt(3)/2 + sqrt(3)/2 = 0

The answer for A is zero.