Question

Period of function |sinx| + | cosx|

Answer 1

Answer:

sin x+ cos x is equal to 1

Answer 2

$\fcolorbox{red}{aqua} {Solution:-}$

$\red{ = > } | \sin(x) | + | \cos(x) |$

$The \: periods \: of \: sin(x) and \: cos(x) \\ are \: both \: 360^{0} \: so \: sin(x) + cos(x) \\ repeats \: on \: any \: interval \: of \: length \\ {360}^{0} . \: Thus 360^{0} \: is \: a \: period \: of \: \\ sin(x) + cos(x). \: The \: question \: is \: \\ then, \: is \: 360^{0} \: the \: period \: of \: \\ sin + cos(x)? \: That \: is, \: is \: 360^{0} \: the \: \\ length \: of \: the \: shortest \: interval \: \\ on \: which \: sin + cos(x) \: repeats? \: \\ This \: is \: where \: a \: graph \: is \: useful. \: </p><p></p><p> \\ \\ I \: plotted \: sin(x) + cos(x) \: for \: x \: \\ from \: -360^{0} \: to \: 720^{0} .$

$From \: the \: graph \: you \: can \: see \: \\ that \: there is \: a \: repeat \: on \: \\ intervals \: of \: length \: 360^{0} \: but \: \\ no \: shorter \: interval \: where \: \\ the \: graph \: repeats. \: Thus \: \\ the \: period \: of \: \\ sin(x) + cos(x) \: is \: 360^{0} . \\ \\ \underline{ \fbox{i \: hope \: it \: helps \: you.}}$