Find exact value of cos(13pi/6)

Answer 1

To find the exact value of cos(13π/6), we can note that 13π/6 is equivalent to 2π + π/6.

Since the cosine function has a period of 2π, the value of cos(13π/6) is the same as the value of cos(π/6).

To find the exact value of cos(π/6), we can use the cosine of a half-angle formula:

cos(π/6) = √[(1 + cos(π/3))/2]
= √[(1 + 1/2)/2]
= √[(3/2)/2]
= √(3/4)
= √3/2.

So, the exact value of cos(13π/6) is √3/2.