Question

If theta lies in the quadrant IV. What can be the value of cos theta ?

Answer 1

Cos(theta) has positive values in quadrants I and IV and it has negative value in quadrants II and III.  To know that you don't have to remember this but to imagine xy coordinate system. In it you draw a circle around the center.

Once you do that for any given angle you project the point which represents crossing of side that defines angle and circle. Now project that dot on x-axis. If projection is on positive side of x-axis, cos of that angle is positive and if it is on negative side it is negative.