The midline is halfway between the extremes; amplitude is the distance from it to either extreme. The period is one complete cycle. y=sin x **Function** | **0 (0)** | **90 ((pi)/(2))** | **180 (pi)** | **270 ((3pi)/(2))** | **360 (2pi)** sin x | 0 | 1 | 0 | -1 | 0 y=asin(bx), a,b>0 Amplitude=a T= 360 b or 2pib **Function** | **Amplitude** | **Period (degrees)** | **Period (radians)** | **Maximum value of y** | **Minimum value of y** y=2sin 6x | 2 | 60 | (pi)/(3) | 2 | -2 y=5sin 2x | 5 | 180 | pi | 5 | -5 y=sin 4x | 1 | 90 | (pi)/(2) | 1 | -1 y=sin(x)/(2) | 1 | 720 | 4pi | 1 | -1 Mark quarter-period steps and the pattern 0,a,0,-a,0. Label the extremes and stop at the stated endpoints. Example: y=3sin2x, 0 <= x 360 Amplitude 3; period 180. Quarter-period points: (0,0), (45,3), (90,0), (135,-3), (180,0). Repeat for the second cycle.

The midline is halfway between the extremes; amplitude is the distance from it to either extreme. The period is one complete cycle.

\(\text{Amplitude}=a\qquad T=\dfrac{360^\circ}{b}\text{ or }\dfrac{2\pi}{b}\)

Mark quarter-period steps and the pattern \(0,a,0,-a,0\). Label the extremes and stop at the stated endpoints.

Example: \(y=3\sin2x\), \(0\le x\le360^\circ\)

Amplitude \(3\); period \(180^\circ\). Quarter-period points: \((0^\circ,0)\), \((45^\circ,3)\), \((90^\circ,0)\), \((135^\circ,-3)\), \((180^\circ,0)\). Repeat for the second cycle.

Sine graphs and period

Sine graphs and period

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