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Determine the sign (positive or negative) of sinA - cosA when A equals (a) 215 deg (b) -634 deg (c) -457 deg. Which choice gives the correct signs for (a),(b),(c)?

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

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

Solution

Using sinA - cosA = sqrt(2) sin(A - 45deg), the sign depends on the quadrant of (A - 45deg) after reduction.

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