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 real-class 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 one-dimensional vibrations and one-dimensional waves having no dissipation. The sinusoid received from graph of y = sin x, is moving along an x-axis to the left by / 2. (More text below video...)
Other useful lessons:
 Tangent of an Angle Graphing Tangent, Cotangent, Secant and Cosecant Functions
(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 & co-domain ( - < 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.
Winpossible's online math courses and tutorials have gained rapidly popularity since their launch in 2008. Over 100,000 students have benefited from Winpossible's courses... these courses in conjunction with free unlimited homework help serve as a very effective math-tutor for our students.
 - All of the Winpossible math tutorials have been designed by top-notch instructors and offer a comprehensive and rigorous math review of that topic. - We guarantee that any student who studies with Winpossible, will get a firm grasp of the associated problem-solving techniques. Each course has our instructors providing step-by-step solutions to a wide variety of problems, completely demystifying the problem-solving process! - Winpossible courses have been used by students for help with homework and by homeschoolers. - Several teachers use Winpossible courses at schools as a supplement for in-class instruction. They also use our course structure to develop course worksheets.

 Copyright © Winpossible, 2010 - 2011 Best viewed in 1024x768 & IE 5.0 or later version