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

1 Answer
May 10, 2018

x=3.14,x=1.25 or x=4.39

Explanation:

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