CAST is the key to this. Starting in the 4th quadrant and moving counter clock wise, write CAST.
IV quadrant - only COS (and its reciprocal SEC) are positive.
I quadrant - All trig functions are positive.
II quadrant - SIN (and CSC) are positive.
III quadrant - TAN (and COT) are positive.
- Condition 1 indicates this is in quadrant I or II.
- Condition 2 (TAN must be positive) eliminates quadrant II (TAN is negative in quadrant II), so it must be quadrant I.
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