Question

what is cos(-npi)?

Answer 1

\[\cos \left( -\theta \right)=\cos \theta \]

Answer 2

\[cos(- \theta) = Cos\theta\]so, \[cos(-n\pi) = cos (n\pi)\]from the graph of cosine of theta and the above relation, the answer is +1 when n is even and -1 when n is odd.

Answer 3

\[\cos \left( 0\pi \right)=1=\left( -1 \right)^{0}\]
\[\cos \left( 1\pi \right)=\cos \pi=-1=\left( -1 \right)^{1}\]
\[\cos 2\pi=\cos \left( 2\pi-0 \right)=\cos 0=1=\left( -1 \right)^{2}\]
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\[\cos( n \pi)=\left( -1 \right)^{n}\]