Answer:
Step-by-step explanation:
Note that 17pi/8 can be rewritten as 16pi/8 + 1pi/8. 16pi/8 represents 2 full rotations around the center and can be ignored if we just want the cosine of the angle 17pi/8. We are left then with 1pi/8.
We need to find the cosine of this angle. Note that 1pi/8 is 1/2 of 1pi/4, so this situation calls for use of the half angle formula
1 + cos Ф
cos Ф/2 = √(---------------). Here Ф = π/4, and half that is ω = π/8, and the
2 cosine of π/4 is 1/√2.
1 + 1/√2 √2 + 1 2 + √2
So we get cos pi/8 = √( -------------- ) = √ ------------- = √ ---------------
2 2√2 4
