I think the answer is  lies between 30 degrees and 60 degrees.

I am giving details in a few minutes.

 

 

As one cordinate is (sin60,0),and p lies withinn the triangle <60.

As another coordinate is (0,cos30),and p lies withinn the triangle

theta>30.

{Draw the figure after drawing x and y-axis, u will get the logic.}

locus of point p will be x² + y² = 1  . a circle    ( as (sin² + cos²) = 1  )
also we can find the equation of the line which forms the triangle with the x and y axes...
y - (3/2)  = ( (3/2) - 0  ) / ( 0 - (3/2) )       X      (x - 0)

 

y = -x + (3/2)

 

 

find points of intersection....

 

as y is cos    and x is sin  acc. to question therefore

cos   = - sin  + (3/2)

solving,

cos  + sin   = (3/2)

divide both sides by 2 and use formula of sin( a + b)

 

we get sin( pi/4  +   )  =  3   /   2 

 

 = pi / 12  , 5 pi / 12     for  1st quadrant  as the triangle is there

 

thus, point p will be ON the triangle for these values of

and also for  = 0 and pi/2 as at these values sin gives x axis and y axis which r the other 2 sides of the triangle.

 

thus  E ( 0 , pi/12)  U  ( 5 pi/12 , pi /2)

 

 

 

PS. check it out by drawing also . my point will become clear to you

 

plz rate me. :)