Solution: First we have to plot y=cosx
So we find the y value for a range of x i.e
x |
y=cosx |
-4π |
1 |
-7 π/2 |
0 |
-3 π |
-1 |
-5 π/2 |
0 |
-2 π |
1 |
- 3π/2 |
0 |
- π |
-1 |
- π/2 |
0 |
0 |
1 |
π/2 |
0 |
π |
-1 |
3π/2 |
0 |
2 π |
1 |
5 π/2 |
0 |
3 π |
-1 |
7 π/2 |
0 |
4 π |
1 |
Corresponding plot of y=cosx is shown here.
Now to transform y=cos(x) to y=1-cos(x/3), in first step we transform cos(x) to cos(x/3). Observation can be made from cos(x) plot that period of one cycle is 2π, hence the period for cos(x/3) would be 3 times to that of cos(x) i.e. 3x2 π=6 π. That means the plot of cos(x/3) would be stretches 3 times to that of cos(x) about x-axis. The plot cos(x/3) is shown below.
Now finally we transform cos(x/3) to 1-cos(x/3) by simply subtracting the plot of cos(x/3) to the dc level of 1 along the y axis or by simply adding the plot of –cos(x/3) to dc level to 1. The plot of 1-cos(x/3) is shown below.
The comparison of plots cos(x), cos(x/3) and 1-cos(x/3) is shown below.
7. Sketch one period of the graph of Y = 1- cos (3x) starting with the...
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1. On the grid below, sketch the function y =sin-tx in red, and sketch y =(sin x)- in purple. If either (or both) of the graphs have asymptotes, show those in green. If you do not have the colors available, label each curve. y=sinx 70 3704 7/2 1- * -1 31 51 37 11 -2014 -- 2672 But4 -- 2. On the grid below, sketch the function y=cos-'x in red, and sketch y=(cos.x) in purple. If either (or both of...
Which of the following represents an equation for this graph? 4+ a) y = -3 cos(3x + 7) - 2 AFAA., b) y = cos(3x + 2) - 2 c) y = {cos(3x ++) - Ž -47 d) y = cos(4x + 7) - Enter
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Sketch the graph of the
functionf(x, y) = 3x+ 2y.Sketch the surface described by the
equationr−|z|= 0.Sketch the graph of the intersection of these two
surface
Sketch the graph of the function f(x, y) = 3x + 2y. Sketch the surface described by the equation r - |2-0. Sketch the graph of the intersection of these two surfaces.
Sketch the graph of the function f(x, y) = 3x + 2y. Sketch the surface described by the equation r - |2-0....
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