Solve each equation on the interval 0≤x<2π .

Question

a) tan(x/2)=√3

b) sin2x=√3/2

Answer 1

tan(x/2)= sqr3

x/2 = arctansqr3 = 60 degrees or pi/3 radians

x = 120 degrees or 2pi/3 radians +

sin2x = (sqr3)/2

2x = arcsin((sqr3)/2) = 60 degrees or pi/3 radians

or 120 degrees or 2pi/3

2x is in quadrant 1 or 2 for the sine to be postivie

x =60/2 or pi/3/2 = 30 degrees or pi/6 radians

or x=120/2 or 2pi/3/2 = 60 degrees or pi/3 radians