This is a free lesson from our course in Trigonometry
This lesson content introduces and walks you through the basic concepts of the sinusoids.
You'll learn it with the help of some examples, practice questions with solution
using video explanations by the instructor that brings in an element of realclass
room experience. The function y = f(x) = sin x and y = f(x)
= cos x is represented by the graph, and the curve is called a sinusoid.
Sinusoid are the wave having a form which, if plotted, would be the same as that
of a trigonometric sine or cosine function. The sine wave may be thought of as the
projection on a plane of the path of a point moving around a circle at uniform speed.
It is characteristic of onedimensional vibrations and onedimensional waves having
no dissipation. The sinusoid received from graph of y = sin x,
is moving along an xaxis to the left by
/ 2. (More text below video...)
(Continued from above) For example: In case of a function f(x) = 2 sin
(3x 
/2) + 1, the values of
a, b, c and d are 2, 3, /2
and 1 respectively. Therefore, its amplitude is 2, phase shift is
/6 units right, vertical
translation is 1 unit up and the period is 2/3.
The main characteristics of the graph of the functions is  the functions have as
a domain & codomain ( 
< x < +
and 1 <=
y <= +1) respectively. These are periodic functions, having the period of 2
. The modified version of these functions can be expressed in the the form f(x)
= a sin (bx + c) + d or f(x) = a cos (bx
+ c) + d, where a, b, c and d are all real numbers and a & b are not equal to
zero.
Points to remember:
The constant 'a' affects the range; which will be [a, a], where a is amplitude
of the sinusoid.
The constant 'b' affects period. The sinusoid, y = a sin (bx + c) + d has a
period of 2/b.
The constant 'c' results phase shift in the graph. This is a horizontal shift to
the left or right. The amount of the phase shift is c/a and it is to the left if
c > 0, to the right if c < 0.
The constant 'd' results in vertical shift of the graph. A graph is shifted up d
units, if d > 0 and down d units, if d < 0.
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