In this video you will learn about modified sine waves. Instead of using sin(x), you'll start using sin(2x), 5sin(3x),12cos(x+4) and so on. You'll learn what each of these new numbers in the new function represent, how they affect its graph (how they move it around), and how to actually graph the new functions. A very important characteristic of sine and cosine functions is that they are periodic. Their graph is formed by repeated patterns. Also, the graph of the sine function has a specific height. Using all these properties, you'll see the amplitude, the period, the domain and the range, and how to apply transformations on the base function sin(x).
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Modified Sine Waves: Asin(Bx+C)+D and Acos(Bx+C)+D
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Transcription: Modified Sine Waves: Asin(Bx+C)+D and Acos(Bx+C)+D
Hi this is www.educator.com and we are going to try more examples of modified sin waves where we start with the basic equation of sin(x) or cos(x) and the graph of sin(x) or cos(x).0000
We introduce these constant which are going to change some of its attributes and we see what that does to the graph.0013
Remember the equation we are working with in general is (a)sin arcos(bx + c) + d and then from each of those values we figured out these various attributes amplitude, period, phase shift and vertical shift.0021
In this particular equation, the amplitude, remember that is just (a) so you read that as 4, the period is 2pi/b , the b is 2 here, so that is 2pi/2 which is pi.0041
The phase shift, that is the strangest one –c/b, that is (–pi/2)/2 or –pi/4.0066
Finally the vertical shift, that is the easier one is -1 here.0085
Again we will start out with the basic sin way, we will work through introducing these attributes one at a time and see how that moves around and create a new function for us.0097