Question

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

Answer 1

If you just use substitution of the largest values and smallest values i.e 270 and 360 or (270+360) and 720, You should get 0,1 therfore the values would be between 0 and 1 inclusive.If you look at the graph here
http://www.mathsisfun.com/algebra/images...
you see at 270, and 360 which is the 4th quadrant the y values doesn't go past 0 to 1 inclusive
and because cos(360+ theta)=cos (theta) the values will continually be the same hence the values of cos theta is between 0 and 1 inclusive

Answer 2

0 or 1 are not answer choices