The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Trigonometric graphs, periods and transformations
Read amplitude, midline, period and full coordinates.
Respect a restricted domain when finding a range.
Sketch tangent branches separately and identify asymptotes.
For \(y=a+b\sin(cx+d)\), amplitude is \(|b|\) and period is \(\displaystyle \frac{2\pi }{|c|}\). Tangent has period \(\displaystyle \frac{\pi }{|c|}\), no amplitude, and is undefined when its cosine denominator is zero. A restricted interval may not attain the full sine or cosine range.