In Exercises $5-14,$ the space is $C[0,2]$ with the inner product $(6).$

$5.$ Show that $sinmt$ and $sinnt$ are orthogonal when $mn.$

$6.$ Show that sin mi and cos $m$ are orthogonat for all pontive integers $m$ and $n.$

$7.$ Show that $||coskt|{|}^2=$ and $||sinkt|{|}^2=$ for $k>0.$