Solve using a calculator find all solutions in 02pi 1 xsinx1

Solve using a calculator, find all solutions in [0,2pi).

1) xsinx=1

2) x^2+2=sinx

3) 2cos^2x=x+1

4) xcosx-2=0

Solution

1. x sinx=1

sinx=1/x

we can break this equation into two equations

y=sin x

y=1/x

If we graph them,the x coordinate of the intersecting points in the region [0,2pi) is the solutions

x= 1.114       x= 2.773