Cos (7 pi/ 12)

Question

Find the exact value of each expression

Answer 1

The best way to answer this question is with the sum formula for cosine. cos (a + b) = cos a * cos b - sin a * sin b cos (7pi/12) = cos (3pi/12 + cos 4pi/12) = cos (pi/4 + pi/3) Good luck and let me know if you still need help!

Answer 2

cos (7pi/12) = cos (7 · 180^o / 12) = cos 105^o ≈ - 0.26
             180^o / 12 = 15^o ---> 15^o · 7 = 105^o

Answer 3

Try using the half angle formula:

cos (x/2) = +/- √[(1 + cos x)/2]

since 7pi/12 = 1/2 (7 pi/6), 

cos (7pi/12) = +/- √[(1 + cos (7pi/6))/2]

I'll leave the rest to the student.