Statement Problem: In which quadrant does the angle t lie if sec(t) > 0 and sin(t) < 0?
Solution:
In quadrant I: All functions are positive there;
In quadrant II: Sine and its reciprocal (cosecant) are positive while others are negative;
In quadrant III: Tangent and its reciprocal (cotangent) are positive while others are negative;
In quadrant IV: Cosine and its reciprocal (secant) are positive while others are negative.
Thus, if
[tex]\sec (t)>0[/tex]then angle t lies on either quadrant I or quadrant IV.
But also;
[tex]\sin (t)<0[/tex]then angle t here lies on either quadrant III or quadrant IV.
Thus, the common quadrant to both condition is quadrant IV.
CORRECT ANSWER: Quadrant IV
