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The exact value of cos(17pi/8) is

User Greg Bell
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2 Answers

1 vote

Answer:

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

User Michael Brohl
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8.3k points
2 votes


(√(2 + \sqrt2))/(2)

User Michael Ninh
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8.1k points