Trigonometry - Trigonometric Graphs and Parameters

Sine Curve, \(y= \sin (x)\),

Sine Curve, \(y=a\sin(b(x+c))+d\), with \(a>0\) and \(b\ne0\). The amplitude is \(a\), the midline is \(y=d\), the maximum and minimum values are \(d+a\) and \(d-a\), and the period is \(2\pi/|b|\). The following graph illustrates the special case \(b=1\), \(d=0\), so it shows \(y=a\sin(x+c)\); its quarter-cycle labels apply to that case.

Steps of Sketching Sine and Cosine Curves

1. Decide the number of complete cycles required. No. of cycles = \(\frac{\text{Given Domain}}{\text{Period}}\)
2. Draw the grids out based of on the number of complete cycles required. Take note that \(4\) grids per cycle.
3. Sketch the curve on the grid.
4. Draw the \(y\)-axis.
5. Mark down the Amplitude and the Period.
6. Finally, draw the \(x\)-axis with respect to the line of equilibrium.

Sketch the graph \(y=3\sin 2x\) for \( 0 \leq x \leq 360^{\circ}\), stating the amplitude and period.