How can I solve the following inequality: \(\displaystyle{6}{\sin{{x}}}{\cos{{2}}}{x}\geq{0}\)

Harold Hoover

Harold Hoover

Answered question

2022-03-27

How can I solve the following inequality:
6sinxcos2x0

Answer & Explanation

kattylouxlvc

kattylouxlvc

Beginner2022-03-28Added 11 answers

If sinxcos2x=0
either sinx=0x=nπ or cos2x=02x must be odd multiple of π2
Else we need sinx>0 and cos2x>0 or sinx<0 and cos2x<0
For, π<x<2π and 2mπ+π2<2x<2mπ+3π2mπ+π4<x<mπ+3p4
So, the intersection is π+π4<x<π+3π4
For 0<x<π
and (2mπ+0<2x<2mπ+π2  or  2mπ+3π2<x<2mπ+2π)
0<x<π
and (mπ<x<mπ+π4  or  mπ+3π4<xmπ+π)

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