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Reduce each of the following to a trigonometric ratio of a positive acute angle less than 45 deg. Which option correctly lists (a) sin(-65 deg), (b) cos(-928 deg), (c) tan 1145 deg, (d) cot(-1054 deg)?

1. (a) -cos 25 deg, (b) -cos 28 deg, (c) tan 5 deg, (d) -cot 26 deg
2. (a) -sin 25 deg, (b) -sin 28 deg, (c) cot 5 deg, (d) tan 26 deg
3. (a) -cos 25 deg, (b) cos 28 deg, (c) -tan 5 deg, (d) cot 26 deg
4. (a) sin 25 deg, (b) -cos 28 deg, (c) tan 5 deg, (d) -tan 26 deg

Correct answer: (a) -cos 25 deg, (b) -cos 28 deg, (c) tan 5 deg, (d) -cot 26 deg

Solution

Each reduced angle is converted to a ratio of an acute angle under 45 deg using periodicity and complementary-angle identities.

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