Question

ind all real numbers that satisfy each equation: cos(x/2) = 1/2

Answer 1

$$ \bf
cos(\frac{x}{2}) = \frac{1}{2}\\
cos^{-1}\left(cos\left(\frac{x}{2}\right)\right) = cos^{-1}\left(\frac{1}{2}\right)
$$

Answer 2

\[\frac{ x }{ 2 }=\frac{ \pi }{ 3 }+2n \pi\]
or
\[\frac{ x }{2 }=\frac{- \pi }{3 }+2n \pi\]
so:\[x=\frac{ 12n \pi+2\pi }{ 3 }\]
or
\[x=\frac{ 12n \pi-2\pi }{ 3 }\]

Answer 3

how do you know if you subtract or add the 2pi or pi

Answer 4

and the answer says 4pi is that just cause its not restricted?

Answer 5

sin & cos with period 2π

Answer 6

n=0,1,2,3,....................
if n=0 ,x=pi/3 or x=-pi/3
if n=1 ,x=7pi/3 or x=-7pi/3
and so on.