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Determine the sign (positive or negative) of sin A + cos A for each angle: (a) A = 140 deg, (b) A = -356 deg, (c) A = -1125 deg.

1. (a) negative, (b) positive, (c) zero
2. (a) positive, (b) positive, (c) negative
3. (a) negative, (b) negative, (c) positive
4. (a) positive, (b) negative, (c) zero

Correct answer: (a) negative, (b) positive, (c) zero

Solution

Using sqrt(2) sin(A + 45 deg): (a) sin185 < 0 (negative), (b) sin49 > 0 (positive), (c) sin360 = 0 (the expression is exactly zero, neither positive nor negative).

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