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Find the average value of the sequence sin²(1 deg), sin²(2 deg), sin²(3 deg),..., sin²(180 deg) (i.e. the mean of sin²(k deg) for k = 1 to 180).

1. 1/2
2. 89/180
3. 91/180
4. 1/4

Correct answer: 1/2

Solution

Since sin² averages to 1/2 over a complete set of equally spaced angles covering a full period, the mean is exactly 1/2.

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