- On \([0, 2\pi )\), the maximum of \(\cos (\theta )\) occurs at \(\answer {0}\).
- On \([0, 2\pi )\), the minimum of \(\cos (\theta )\) occurs at \(\answer {\pi }\).
If we shift the domain of \(\cos (\theta )\), then the minimum and maximum should follow the shift.
Shifted Domain
Define \(W(m) = \cos \left (m - \frac {\pi }{6} \right )\).
Which interval would we focus on when analyzing \(W(m)\)?
\[ \left [ \answer {\frac {\pi }{6}}, \answer {\frac {7\pi }{6}} \right ) \]
Where does the maximum of \(W(m)\) occur?
\[ m = \answer {\frac {\pi }{6}} \]
Where does the minimum of \(W(m)\) occur?
\[ m = \answer {\frac {7\pi }{6}} \]