SOLUTION: Let f(x)=sin x, g(x)=cos x, and h(x)=2x. Find the exact value of each expression. Do not use a calculator. (A) g(5pi/6+pi/6)=g(5pi/6)+g(pi/6) (B) (h^(degree)f)(11pi/4) P

Question 853151: Let f(x)=sin x, g(x)=cos x, and h(x)=2x. Find the exact value of each expression. Do not use a calculator.
(A) g(5pi/6+pi/6)=g(5pi/6)+g(pi/6)

(B) (h^(degree)f)(11pi/4)
Please I need help with this!!
Answer by harpazo(655) (Show Source): You can put this solution on YOUR website!

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.

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