Graphing Trig Functions
Date: 05/03/97 at 14:45:08 From: Nem Subject: Trigonometric graphing Dear Dr. Math, To graph the equation y = 3sin4x-3, I know I have to find the amplitude, period, and vertical or phase shift. I know the amplitude is 3, and the period is pi/4, but do I have to factor out the 4 from 4x-3 before I can find the vertical shift, or is it simply 3 down? Thank you.
Date: 05/03/97 at 21:55:34 From: Doctor Scott Subject: Re: Trigonometric graphing Hi Nem: You are absolutely right that in order to graph the equation you need to determine the amplitude, period, vertical, AND phase (or horizontal) shift. Remember that the general form of a sinusoidal function (a sine or cosine curve) is: y = a + b*sin[c(x-d)] In this form: a is the VERTICAL SHIFT b is the AMPLITUDE d is the HORIZONTAL SHIFT (or PHASE SHIFT) c is the FREQUENCY (which determines the period) Now, your example, y = 3sin4x - 3 means the same as y = -3 + 3sin(4x). (Unless the 4x-3 is in parentheses, which we will discuss below). This means that we know that: a = -3 (Vertical shift of 3 down) b = 3 (Amplitude of 3) c = 4 (The period is 2pi/4 = pi/2) The period of a "normal" sine curve is 2pi, so here we will see 4 sine curves in the interval [0, 2pi), and thus the period of this curve is 2pi/4 or pi/2. d = 0 (No phase shift) If, however, the original function is y = 3sin(4x - 3), we could rewrite this as y = 3sin[4 (x - 3/4)] by factoring the 4 out of the (4x-3) expression. Then, a = 0 (No vertical shift) b = 3 (Amplitude of 3) c = 4 (The period is 2pi/4 or pi/2) d = 3/4 (A horizontal shift of 3/4 unit to the right.) Good luck! -Doctor Scott, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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