solve cos (7x)=0 on the interval [0,2pi/7]

Question

anonymous · Answer

Let's replace $7x$ with another variable -- how about $u$? Can you solve $\cos u=0$ on the interval $[0,2\pi]$?

anonymous · Answer

Phew thanks for the reply...So  cosx=0 at 0 and 2pi right??

anonymous · Answer

No... try sketching a unit circle.

anonymous · Answer

oh its at pi/2, 3pi/2...

anonymous · Answer

@tanentrahan indeed. Now convert back to $x$. Remember, $u=7x$ so $x=\frac17u$. Since we solved for $u$ in $[0,2\pi)$ we will get $x$ in $\left[\frac07,\frac{2\pi}7\right)=\left[0,\frac{2\pi}7\right)$.

anonymous · Answer

Thanks!!! I'm not sure if i completely understand what happened though. We isolated the "x" and solved for it right??

anonymous · Answer

So for this one cos(7x)=-1 the interval being 0, pi/2 our x value is -1/7 right?