Question

Find the maximum positive x such that
a) sin x=0 b) cos 2x-1/2=0 c) sin (x^2 + x + 4)=0

Answer 1

\(\sin x=0\) for \(x=2n\pi\), for \(n=0,\pm1,\pm2,...\). There's no maximum for the first one, unless you restrict the domain.

Is the second one \(\cos2x-\dfrac{1}{2}=0\) or \(\cos\left(2x-\dfrac{1}{2}\right)=0\) ?

The third is a lot like the first, in that
\[\sin(x^2+x+4)=0\]
for
\[x^2+x+4=2n\pi,~\text{for }n=0,\pm1,\pm2,...\]