For what values of θ is sinθ < cosθ when 0 ≤ θ < π?

Question

the answer is set up as __ ≤ θ < __

Answer 1

In the 2nd quadrant sinx is positive and cosx is negatvie, so rule out 2nd quadrant ahgles.

IN the 1st quadrant ask yourself where does sinx = cosx,? Only at pi/4. On the unit circle visualize angles starting at 0 and moving towards pi/4. At 0, sinx = 0 and cosx = 1. At pi/6 (for example), the y coordinate (sin x) the point on the unit circle is .5, but x coordinate is √3/2 (0.866). As the angle moves past pi/4, the y coordinates become greater then the x-coordinates.

Answer 2

From 0 to π/4.

The best way to see this is to use your graphing calculator to graph both functions on the same axis.