identify the quadrant in which 0 lies.

sin < 0 and sec > 0

Sin < 0-----> quadrant 3 and 4

Sec > 0 ---- quadrant 1 and 4

sec = 1/cos

Answer is quadrant 4

sin negative, cosine positive?

sin is negative III, IV
cosine positive I, III

4/7/206

4/7/2006

To identify the quadrant in which 0 lies based on the given conditions, we need to look at the properties of the trigonometric functions in each quadrant.

First, let's consider the sign of the sine function (sin). When sin is negative (sin < 0), it means that the angle is in either the third or fourth quadrant.

Next, let's consider the sign of the secant function (sec). When sec is positive (sec > 0), it means that the angle is in either the first or fourth quadrant.

Since we are given that sin < 0 and sec > 0, we can determine that the angle 0 lies in the fourth quadrant.

To understand why, let's break down the conditions:

sin < 0: In the third quadrant, sin is negative.
sec > 0: In the first quadrant, sec is positive.

Thus, considering both conditions together, we can conclude that the angle 0 lies in the fourth quadrant.