- On \([0, 2\pi )\), the maximum of \(\sin (\theta )\) occurs at \(\answer {\frac {\pi }{2}}\).
- On \([0, 2\pi )\), the minimum of \(\sin (\theta )\) occurs at \(\answer {\frac {3\pi }{2}}\).
If we shift the domain of \(\sin (\theta )\), then the minimum and maximum should follow the shift.
Shifted Domain
Define \(f(t) = \sin \left (t + \frac {\pi }{3} \right )\).
Which interval would we focus on when analyzing \(f(t)\)?
\[ \left [ \answer {-\frac {\pi }{3}}, \answer {\frac {5\pi }{3}} \right ) \]
Where does the maximum of \(f(t)\) occur?
\[ t = \answer {\frac {\pi }{6}} \]
Where does the minimum of \(f(t)\) occur?
\[ t = \answer {\frac {7\pi }{6}} \]