Question

How do I find the zeros of this function without graphing.
f(x)=3+3 cos (x-π)
I know the graph has lot of zeros. How would I find at least two and explain they repeat periodically?
Thanks

Answer 1

\[f \left( x \right)=3+3\cos (x-\pi)=3+3\cos \left\{ -\left( \pi-x \right) \right\}=3+\cos \left( \pi-x \right)=3-3\cos x\]
\[3-3\cos x=0,\cos x=1=\cos \left( 2n+1 \right)\frac{ \pi }{ 2 },x=\frac{ n \pi }{ 2 }\]

Answer 2

3+3cos{−(π−x)}=3+cos(π−x)=3−3cosx

Good start, thanks but I don't understand why is this step valid. Why does the minus sign hace to change.

Answer 3

\[\cos \left( -x \right)=\cos x,\cos \left( \pi-x \right)=-\cos x\]

Answer 4

Okay, I got it. Thanks again

Answer 5

yw