Consider $f(x)=3cos(x)$ and $g(x)=4sin(x)$ The graph of $h(x)=f(x)+g(x)$ is a sinusoid$.$

$($a$)$ Find the period and amplitude of the graph of $h(x).$

$($b$)$ Note that $h(x)$ can be written as $y=$Acos$(x-D),$ for some A and $D.$ Find A and D$.$

$($c$)$ If instead, you had $f(x)=$pcos$(x)$ and $g(x)=$qsin$(x),$ find A and $D$ such that $h(x)=f(x)+g(x)=$Acos$(x-D).$