Solve (sinx)(tanx) = 3sinx for 0 < x < 2pi. Round your answers to the nearest hundredth of a radian ?

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Answer 1 · 2018-05-10T04:44:31

$x=3.14,x=1.25 or x=4.39$

Here,

$sinxtanx=3sinx,where, 0 < x < 2pi$

$=>sinxtanx-3sinx=0$

$=>sinx(tanx-3)=0$

$=>sinx=0 or tanx-3=0$

$sinx=0 or tanx=3$

$(1)sinx=0,where, 0 < x < 2pi$

So, $color(red)(x=pi=3.14^R$

$(2)tanx=3 > 0=>I^(st)Quadrant or III^(rd)Quadrant$

$(i)I^(st)Quadrant=>0 < x <= pi/2$

$=>color(blue)(x=tan^-1(3)=1.25^R=(71.57)^circ$

$(ii)III^(rd)Quadrant=>pi <= x <= (3pi)/2$

$=>color(blue)(x=pi+tan^-1 (3)=4.39^R=(251.57)^circ$