• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

Investigating the Graphs of Sine Function.

Extracts from this document...

Introduction

Investigating the Graphs of Sine Function

The task of this assignment is to investigate various sine graphs and recognise patterns and generalisations.

Part 1

Look at the graph of y = sin x.

Compare the graphs of y = 2 sin x ; y = 1/3 sin x ; y = 5 sin x.

Investigate other graphs of the type y = A sin x.

How does the shape of the graph vary as A varies?

Express your conjecture in terms of

1. transformation(s) of the standard curve y = sin x.
2. characteristic(s) of the wave form.

To do the graphs including graph y = sin x, first I used my TI-83 Graph Calculator to have an idea of how the sketch should look. Then, for the real graph I used in the computer, a program called “Omnigraph” that is ideal for drawing graphs in the Cartesian set of axis, and that could be adjusted to draw trigonometric graphs as well with a suitable scale. This program provides all the facilities needed for them to be clear and accurate.

Graph to show the curve of y = sin x This is the graph of y = sin x that would be the base curve used to compare all the other curves I would be drawing in this assignment in order to investigate how does different coefficients affect the position and shape of the sine graph. I am asked to compare y = sinx

Middle

x represents an angle.

The graph below shows three waves where B has been varied in order to investigate how this change affects the wave’s position and shape.

Graph to show y = sin 2 x ; y = sin 1/3 x and y = sin 5 x In order to investigate what is the effect of B on the y = sin x curve, the graph above has to be compared with the first graph of this assignment, the base graph of y = sin x. It can be noticed that B affects the period of the wave. When varying B, it can be noticed that the wave’s period is B times as short as the base wave’s period. In other words, the inverse of B (1/B) is equal to the base wave talking in period terms.

For example, in the graph of y = sin 2 x shown above, the period is two times as short as the period of the base graph of y = sin x. Now, the period is only 180º which is half of the base or original period.

Another example, where it happens exactly the same thing, is in the graph of y = sin 1/3 x that is also shown above. The period is 1/3 times short, or in other words, 3 times as long as the base wave’s period. In this case, the period is 1080° because 360° * 3 = 1080°.

Conclusion

d, then the period will be d times as long as the one in the base graph of y = sin x. C being a fraction is only a very little angle, the movement will be to the same direction, but almost insignificant as the number is so little.
Part 5

How is the graph of y = cos x linked to the graph of y = sin x?

What is the relationship between these functions?

Part 5 is to compare and contrast the graph of sine and cosine.

Graph to show y = sin x and y = cos x It can be noticed that both waves have the same amplitude and period, but a different position. It seems as if y = sin x has been added 180º to the x, so there has been a translation along the x axis of the vector    180

0

It doesn’t matter if 180° is negative or positive because it will be the same as the period is 360° and 180° is its half.

To extend this investigation, and prove that it happens in every single graph of sine and cosine because all of them have the same characteristics, I am going to draw a graph showing this.

Graph to show y = - ½ sin 3 (x – 90º) and y = - ½ cos 3 (x –90º) This graph proves what it was stated before as it can be clearly noticed that both waves have the same shape which includes amplitude and period, but the only that changes is position by 180º, or in other words, by a translation of  180

0

NAME        Page                 09/05/2007

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

Related International Baccalaureate Maths essays

1. Extended Essay- Math

@"Â-HFBï¿½ï¿½P8Qï¿½Iï¿½ Z" N Bï¿½DQ\$&!ï¿½D(<hï¿½d\$8Aï¿½...E'ï¿½"ï¿½ï¿½ %''ï¿½"NEb< @"Â-HFBï¿½ï¿½P8Qï¿½Iï¿½ Z" N Bï¿½DQ\$&!ï¿½D(<hï¿½d\$8Aï¿½...E'ï¿½"ï¿½ï¿½ %''ï¿½"NEb< @"Â-HFBï¿½ï¿½P8Qï¿½Iï¿½ Z" N Bï¿½DQ\$&!ï¿½D(<hï¿½d\$8Aï¿½...E'ï¿½"ï¿½ï¿½ %''ï¿½"NEb< @"Â-HFBï¿½ï¿½P8Qï¿½Iï¿½ Z" N B(c)ï¿½ï¿½ï¿½Üï¿½'...(c)! Rï¿½Pï¿½Vï¿½ï¿½"'"tï¿½ï¿½ï¿½åï¿½(r)wy*@ï¿½ï¿½''ï¿½ï¿½N'ï¿½uï¿½ï¿½aï¿½ï¿½ï¿½mÛ¶ï¿½ï¿½vssBï¿½2l(]ï¿½ï¿½...ï¿½ï¿½ï¿½/^1/4ï¿½ï¿½ï¿½6ï¿½ï¿½3/4~%)7!`ï¿½0ï¿½>ï¿½ï¿½bvvvï¿½Úµï¿½ï¿½ï¿½{ï¿½ΝfÍï¿½ï¿½ï¿½XXXï¿½lï¿½ï¿½"xFï¿½,ï¿½ï¿½ï¿½ï¿½Ñ£ï¿½ï¿½ï¿½ï¿½kï¿½ï¿½ï¿½/Oï¿½<Ù¹sï¿½P>,, 3ï¿½_ï¿½"ï¿½PD(ï¿½)ï¿½Qï¿½F/1/2ï¿½'1/21/2=ï¿½ï¿½){ï¿½ï¿½ï¿½<ï¿½(ï¿½_ï¿½"ï¿½PD(ï¿½)ï¿½"{ï¿½ï¿½ï¿½(ï¿½ï¿½~ï¿½ï¿½ï¿½Wï¿½rï¿½Fï¿½|(ï¿½(c)ï¿½Fï¿½ï¿½--ï¿½ï¿½ï¿½ï¿½ï¿½(c)Sï¿½ï¿½ï¿½ï¿½ _yï¿½Mï¿½Zï¿½ï¿½^xRð±³³"ï¿½0<)ï¿½ï¿½Tï¿½%ï¿½Fï¿½ï¿½>{ï¿½ï¿½ï¿½ï¿½"jï¿½ï¿½pï¿½("ï¿½"-ï¿½D2ï¿½ @"Âï¿½HLBï¿½ ï¿½Pxï¿½ï¿½Hpï¿½ 'ï¿½"1 - Bï¿½AK\$#!ï¿½ D(ï¿½(ï¿½ï¿½\$x@ï¿½... -'ï¿½"'ï¿½pï¿½("ï¿½"-ï¿½D2ï¿½ @"Âï¿½HLBï¿½ ï¿½Pxï¿½ï¿½Hpï¿½ 'ï¿½"1 - Bï¿½AK\$#!ï¿½ D(ï¿½(ï¿½ï¿½\$x@ï¿½... -'ï¿½"'PH#(ï¿½ï¿½ï¿½ï¿½f(tm)(r)ï¿½ï¿½vï¿½.6}ï¿½ï¿½'ï¿½ dee...@"HApl<;88ï¿½_"ï¿½Æï¿½ï¿½3/4]ï¿½ï¿½ï¿½µ\$Hï¿½ï¿½[ï¿½nï¿½"ï¿½]ï¿½&ï¿½J@@ï¿½ï¿½ï¿½ï¿½Pï¿½6ï¿½*(ï¿½ L'(tm)(tm)yï¿½ï¿½ï¿½3gï¿½\ï¿½rï¿½ï¿½"ï¿½ï¿½ï¿½ï¿½ï¿½Ô-"*Eï¿½hdBNï¿½brrrï¿½8(.1/4xx+ï¿½_Qï¿½ï¿½Å¥kï¿½(r)ï¿½Û·G ï¿½ï¿½jï¿½+ï¿½9}ï¿½4ï¿½ ï¿½ï¿½Fï¿½p2ï¿½@/4""Wï¿½ï¿½Dï¿½"ï¿½ï¿½ï¿½)\&ï¿½ï¿½]ï¿½)p1jCN" ï¿½ï¿½ï¿½-[ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½Fï¿½(r)(c)ï¿½(tm)...ï¿½6ï¿½899Í;ï¿½ï¿½ï¿½1/4(r)(r)(r)xï¿½1ï¿½ï¿½80ï¿½ï¿½1/2*ï¿½\$ï¿½ï¿½Bsxï¿½ 8pï¿½ï¿½Rï¿½Fuï¿½ï¿½ï¿½ï¿½ï¿½ï¿½|ï¿½2ï¿½!3/48~ï¿½8ï¿½ ï¿½ ï¿½ï¿½ï¿½ï¿½@πï¿½0yï¿½A7 4ï¿½/\ï¿½ ï¿½ï¿½<ï¿½ ï¿½ ï¿½( j*ï¿½;D(ï¿½cUqN1/4ï¿½x[6oÞï¿½ ï¿½ï¿½q<{ï¿½lï¿½-=zà§²ï¿½bÒ¤ï¿½7&ï¿½Kï¿½--ï¿½ o> ï¿½0!ï¿½ï¿½ {ï¿½ï¿½9qï¿½ï¿½2hZxï¿½Asxï¿½(tm)pGï¿½"ï¿½ï¿½ï¿½B\$0ï¿½W ï¿½^1/2z ï¿½[6'=ï¿½Bï¿½E 'ï¿½ï¿½ï¿½ï¿½ï¿½Úµ #ï¿½ F*.ï¿½ï¿½0Cï¿½Nyï¿½ï¿½ï¿½(r)

2. Math IA type 2. In this task I will be investigating Probabilities and investigating ...

such that one player wins 4 of the first 4 points and there then this would not be a game of 5 points. Therefore it is important to not include the last point in the calculation because it is the winning point and is always the last point and therefore

1. Investigating the Graphs of Sine Functions.

(b) characteristics of y= sin x: the curve is symmetric with the origin, it is an even function, and has infinite intercepts at multiples of , as well as infinite maximum and minimum points at - and .

2. Math IA Type 1 In this task I will investigate the patterns in the ...

* Also I found that D is inversely related to the absolute value of a and not to a itself. Quadrant 2 Example 1 Function seen in the graph: [In green] [In black] [In red] Again, the parabola of

1. Function Transformation Investigation

Expression - will be a vertical translation,up, by -b. Using the stated method above, we can calculate the translation of. First of all let's move all the input and output altering numbers to the left side of the equation: 3 is added to the input and 2 to the output.

2. Mathematics Higher Level Internal Assessment Investigating the Sin Curve

without changing the vertical position of the curve. The reason that this horizontal stretch occurs is because all the values of the curve are multiplied by a factor of . This means that a lower value of is required to get the same value as the original graph.

1. Investigating Sin Functions

Let me pose a question, what of negative numbers?? Since A would be decreasing to get negative numbers, would that make the graph shrink, because that follows logically with the above conclusions? Well let's see... Y = sin(x) Y = -1sin(x) As we observe these graphs, we notice that the negative number placed in front of sin (x)

2. Analysis of Functions. The factors of decreasing and decreasing intervals (in the y ...

Power functions are not periodic because a periodic function repeats function values after regular intervals. It is defined as a function for which f(x+a) = f(x), where T is the period of the function. In the case of power functions, it can't be a periodic function is that there is no definite or constant period like "a". • Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to
improve your own work 