What is the angle of intersection of $$[|\sin x| + |\cos x|]$$ And the curve $$ x^2 + y^2 = 5 $$ where $[n]$ denotes greatest integer function.
This is a homework question. I have tried to find the intersection of these two curves but i am unable to do so. In the solution booklet provided , the first curve has been changed to $y = 1 $ without any explanation. Can anyone please explain me this ?
2026-04-04 03:20:38.1775272838
Angle of intersection of the given curves.
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1) From the above hint it is proved that [|sinx+cosx|]=1...(eq i)
Again,if we find the local extremum for the above equation(eq i) [0<=x<=(pi/2)], we get the maximum value as (root 2)=1.414(approx), minimum value=1.
So,in this way we can also get that [|sinx+cosx|]=1.
Thus y=[|sinx|+|cosx|]=1
2) Now, find the point of intersection between y=1 & x^2+y^2=5
3) Since one of the curve is a circle, find the equation of the tangent to the circle (at the point of intersection of the straight line & the circle).
4) Find the slopes of the tangent & the straight line.
5) Now find the angle between them by using the equation [|(a-b)/(1+ab)|] (where a & b are the slopes of the tangent & straight line respectively)