For what value(s) of x, 0<x<pi/2, is sinx<cosx

If you have a graphing calculator and any hesitation at all about this, the best way to go is to graph. Make sure your calculator is in radians mode!

Between and , the red curve is below the blue curve until . After that point, the lines cross.

Without a calculator, you should still be able to reason this one out if you remember a few basics:

*(or in degrees, )*

*(or in degrees, )*

*(or in degrees, )*

From the above, you know that the cosine curve is higher than the sine curve at , and that the curves intersect at . They don’t intersect again before .