To find cos(π/16), we can use the half-angle identity for cosine. The half-angle formula states:
cos(θ/2) = √((1 + cos(θ)) / 2)
In this case, we need to express π/16 in a way that we can apply this identity. We can see that:
π/16 = (π/8) / 2
Thus, we can find cos(π/8) first. To calculate cos(π/8), we apply the half-angle formula again using π/4:
cos(π/8) = √((1 + cos(π/4)) / 2)
Since cos(π/4) = √2/2, we can substitute this value into the half-angle formula:
cos(π/8) = √((1 + √2/2) / 2)
Now, substitute cos(π/8) back into the half-angle formula to find cos(π/16).
So, using the value we derived, we have:
cos(π/16) = √((1 + cos(π/8)) / 2)
Substituting the computed value for cos(π/8) into this formula will yield the final value for cos(π/16).
In summary, cos(π/16) can be calculated using the half-angle identities systematically until you reach the desired angle.