find all solutions

Question

Find all solutions exactly on the interval 0≤θ<2⁢π.

2sin (2 0)=1

Answer 1

if the problem reads

2sin2x =1 (x=theta)

then divide by 2

sin2x = 1/2

2x= 30 degrees

x =15 degrees+ 180n where n = any integer

x = 15, 195 degrees or 15-360= -345 degrees

but you want x between 0 and 360 degrees, so

x = 15 degrees = 15(pi/180) = pi/12 radian

or 195 degrees = 195(pi/180) = pi + pi/12 = 13pi/12 radians

Answer 2

sin(2θ) = 1/2; 2θ = π/6 + 2πn; θ = π/12 + πn, or 2θ = 5π/6 + 2πn; θ = 5π/12 + πn;

Then set n = 0 θ = π/12 or θ = 5π/12;

n = 1; θ = 13π/12 or θ = 17π/12