Question

In which quadrant does the angle t lie if sec(t) > 0 and sin(t) < 0?

Answer 1

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

`\sec (t)>0`

then angle t lies on either quadrant I or quadrant IV.

But also;

`\sin (t)<0`

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