Question

Solve
Sin(2theta)=1/2

Answer 1

sin(2theta)=1/2

sin(x)=α
x=(-1)^k arcsin α+πk

2theta=(-1)^k arcsin 1/2 + πk k∈Z
arcsin 1/2= π/6
2theta=(-1)^k π/6 + πk k∈Z
theta=(-1)^k π/12 + πk/2 k∈Z

Answer 2

Just change the fraction into an equivalent in the sine function.


`sin(2\theta)= (1)/(2) \\ sin(2\theta)=sin( ( \pi )/(6)+2k \pi ) \\ 2\theta=( \pi )/(6)+2k \pi \\ \theta=( \pi )/(12)+k \pi \\ \\ sin(2\theta)= (1)/(2) \\ sin(2\theta)=sin( ( 15\pi)/(18)+2k \pi ) \\ 2\theta=( 15\pi )/(18) +2k \pi \\ \theta=( 15\pi )/(36)+k \pi`

Therefore:


`\boxed \theta=( \pi )/(12)+k \pi ~or~ \theta=( 15\pi )/(36)+k \pi, k \epsilon Z)`

If you notice any mistake in my english, please let me know, because i am not native.