Question

how do you find all solutions for the equation sin (4x)=1/2

Answer 1

\[
\sin(4x) =\frac 12 =\sin(\pi/6)
\]

Answer 2

\[ 4 x = \frac \pi 6 + 2 k\pi
\\
4 x = \pi -\frac \pi 6 + 2 k\pi
\]

Answer 3

\[x = \frac \pi {24} + k\frac \pi 2
\\
x =\frac{ 5 \pi} {24} + k\frac \pi 2

\]

Answer 4

i forgot to put over the interval of [0.2π) so this is 2 of them but not all of them but i think i get how to do the rest thankyou

Answer 5

yw