×

Hello! Socratic's Terms of Service and Privacy Policy have been updated, which will be automatically effective on October 6, 2018. Please contact hello@socratic.com with any questions.

How do you find the exact values of cos 15 using the half angle formula?

1 Answer
Aug 30, 2015

Answer:

#color(red)(cos15 = sqrt(2 +sqrt3)/2)#

Explanation:

The cosine half-angle formula is

#cos(x/2) = ±sqrt((1 + cos x) / 2)#

The sign is positive if #x/2# is in the first or fourth quadrant and negative if #x/2# is in the second or third quadrant.

#15°# is in the first quadrant, so the sign is positive.

#15= 30/2#

#cos15 = cos(30/2) = sqrt((1+cos30)/2)#

#cos15 = sqrt((1 + sqrt3/2)/2) = sqrt((2 + sqrt3)/4)#

#cos15 = sqrt(2 +sqrt3)/2#