Question

suppose theta is an angle in standard position with cos(theta)>0. In which quadrant could the terminal side of theta lie?

Answer 1

If cos (theta) > 0 , then this means that the angle theta could be located either
in the first or fourth quadrant.

Theta's value could be from 0 to 90 (1st quadrant)
Or could be from 270 to 360 (4th quadrant)

In those quadrants, the x component (which is equal to the magnitude of the vector times cos (theta) ) is positive.