Compute ∑ k = 0 180 cos 2 ⁡ 2 k ∘

Logan Wyatt

Logan Wyatt

Answered

2022-07-02

Compute k = 0 180 cos 2 2 k

Answer & Explanation

Keely Fernandez

Keely Fernandez

Expert

2022-07-03Added 14 answers

Hint: Observe that for the first quadrant, we have
cos 2 2 + cos 2 4 + + cos 2 88 + cos 2 90 = cos 2 2 + cos 2 4 + + cos 2 44 + sin 2 44 + sin 2 42 + + sin 2 2 + 0 = 22.
sebadillab0

sebadillab0

Expert

2022-07-04Added 3 answers

S = r = 0 180 cos 2 2 r
2 S = r = 0 180 ( 1 + cos 4 r ) = 181 + r = 0 180 cos 4 r
Using cos when angles are in arithmetic progression,
r = 0 180 cos 4 r = cos ( 2 180 ) sin ( 2 181 ) sin 2 = + 1

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