I’ve slapped together this simple VPython program to introduce sinusoidal functions to my pre-Calculus students.

- Left and right arrow keys increase and decrease the frequency;
- Up and down arrow keys increase and decrease the amplitude;
- “a” and “s” keys increase and decrease the phase.

The specific functions shown on the graph are based on the general function:

where:

- A — amplitude
- F — frequency
- P — phase

When I first introduce sinusoidal functions to my pre-Calculus students I have them make tables of the functions (from -2π to 2π with an interval of π/8) and then plot the functions. Then I’ll have them draw sets of sine functions so they can observe different frequencies, amplitudes, and phases.

from visual import * class sin_func: def __init__(self, x, amp=1., freq=1., phase=0.0): self.x = x self.amp = amp self.freq = freq self.phase = phase self.curve = curve(color=color.red, x=self.x, y=self.f(x), radius=0.05) self.label = label(pos=(xmin/2.0,ymin), text="Hi",box=False, height=30) def f(self, x): y = self.amp * sin(self.freq*x+self.phase) return y def update(self, amp, freq, phase): self.amp = amp self.freq = freq self.phase = phase self.curve.y = self.f(x) self.label.text = self.get_eqn() def get_eqn(self): if self.phase == 0.0: tphase = "" elif (self.phase > 0): tphase = u" + %i\u03C0/8" % int(self.phase*8.0/pi) else: tphase = u" - %i\u03C0/8" % int(abs(self.phase*8.0/pi)) print self.phase*8.0/pi txt = "y = %ssin(%sx %s)" % (simplify_num(self.amp), simplify_num(self.freq), tphase) return txt def simplify_num(num): if (num == 1): snum = "" elif (num == -1): snum = "-" else: snum = str(num).split(".")[0]+" " return snum amp = 1.0 freq = 1.0 damp = 1.0 dfreq = 1.0 phase = 0.0 dphase = pi/8.0 xmin = -2*pi xmax = 2*pi dx = 0.1 ymin = -3 ymax = 3 scene.width=640 scene.height=480 xaxis = curve(pos=[(xmin,0),(xmax,0)]) yaxis = curve(pos=[(0,ymin),(0,ymax)]) x = arange(xmin, xmax, dx) #y = f(x) func = sin_func(x=x) func.update(amp, freq, phase) while 1: #theta <= 2*pi: rate(60) if scene.kb.keys: # is there an event waiting to be processed? s = scene.kb.getkey() # obtain keyboard information #print s if s == "up": amp += damp if s == "down": amp -= damp if s == "right": freq += dfreq if s == "left": freq -= dfreq if s == "s": phase += dphase if s == "a": phase -= dphase func.update(amp, freq, phase) #update_curve(func, y)

**Citing this post**: **Urbano**, L., 2014. Sine Curves, Retrieved April 27th, 2017, from *Montessori Muddle*: http://MontessoriMuddle.org/ .**Attribution (Curator's Code )**: Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.