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Math Investigation - Sine Law

Extracts from this document...

Introduction

Part 1

Look at the graphs of y = sin x

Compare the graphs of:

y = sin x

y = 2sin x

y = 1/3sin x

y = 5sin x

The difference between all these graphs is a variable known as A, or amplitude of wave.

When A > 1, the graph stretches vertically.

When 0 < A < 1, the graph compresses vertically.

Also, A is the number that manipulates how far the graph compresses or stretches to. For example, in the graph of y = 2sin x, the graph stretches out to +2 and down to -2. The characteristics of the waveform are altered because of this. The range of the graph is increased or decreased in conclusion.

The domain and range of the graphs are:

y = sin x

D: {x| xεR}

R: {y| -1 < y < 1, yεR}

y = 2sin x

D: {x| xεR}

R: {y| -2 < y < 2, yεR}

y = 1/3sin x

D: {x| xεR}

R: {y| -1/3 < y < 1/3, yεR}

y = 5sin x

Middle

y = sin x?

The C variable in y = sin (x + C) is a variable that creates a horizontal translation.

In example, if C is substituted with 90, the equation becomes y = sin (x + 90):

y = sin x

y = sin (x+90)

It is evident that the entire graph shifted to the left by 90 unit. This can conclude that the amount that the graph moves by is by C, except it moves the direction opposite to the symbol in front of it. In this case, C, 90, caused the graph to move to the left by 90. This said, if C was -90, the graph would move to the right by 90 units. The range for y = sin (x + C) is not affected by the translation.

The domain and range of the graphs are:

y = sin x

D: {x| xεR}

R: {y| -1 < y < 1, yεR}

y = sin (x+90)

D: {x| xεR}

R: {y| -2 < y < 2, yεR}

Part 3

Conclusion

+ 90o)

I predicted this function as a vertical stretch since A > 1. The C in the graph translates the line 90 units to the left. There is no D in this function.

D: {x| xεR}

R: {y| -3 < y < 3, yεR}

y = ½sin x + 3

I predicted this function as a vertical compression because A < 1. There is no C present in this function. The D in the function moves the line up 3 units on the y-axis.

D: {x| xεR}

R: {y| -2½ < y < 3½, yεR}

Part 5

The graph of y = cos xand the graph of y = sin xis almost the exact same thing. The only difference is that the same graph would be translated 90o to the left if it involved the cos function.

Essentially, cos (x) = sin (x +90o).

Since this is true, it is conclusive that sine is a very versatile function with many altering variables.

y = cos x

y = sin (x + 90o)

*Although it is not completely evident, the two lines are overlapping, as I had predicted.

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

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1. Extended Essay- Math

ï¿½_ï¿½ tIME ï¿½ 2-ï¿½ï¿½ IDATxï¿½ï¿½lgï¿½Ç.Hï¿½ï¿½Jï¿½ \$ï¿½Urï¿½vËªï¿½ZicÊªï¿½ï¿½ï¿½uï¿½ï¿½ï¿½Õï¿½ï¿½:ï¿½Iï¿½p"'ï¿½uï¿½n7ï¿½Sï¿½d"m"ï¿½ï¿½%]ï¿½\$T'J...ï¿½ï¿½ï¿½Ó¶8ï¿½cï¿½"ï¿½Ø¨EvUP-"8ZVï¿½hsï¿½dï¿½(tm)_-{Æï¿½ï¿½ï¿½(ï¿½ï¿½ï¿½xï¿½_ï¿½yï¿½ï¿½}çï¿½ï¿½Eï¿½\Ü§ï¿½[email protected]@ï¿½KPï¿½ï¿½[email protected]@ï¿½KPï¿½QSï¿½ï¿½Ô g:"ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½^ï¿½ï¿½ï¿½"4?cï¿½ï¿½dKï¿½^1/2ï¿½" ï¿½@ï¿½KPï¿½ï¿½[email protected]@ï¿½KPï¿½ï¿½[email protected]@Uï¿½T(ï¿½#ï¿½[ï¿½Õ¶Ö¦ï¿½!ï¿½ï¿½ï¿½ï¿½l - ï¿½ï¿½bï¿½Cï¿½ï¿½-ï¿½ï¿½6T5ï¿½Aï¿½ï¿½-ï¿½ï¿½Xï¿½ï¿½ Ú\ï¿½2 v5ï¿½ï¿½ï¿½ï¿½ï¿½ Pï¿½@.Aï¿½&ï¿½ï¿½ ï¿½"(c)ï¿½"ï¿½jï¿½ï¿½ Pï¿½@.ï¿½ï¿½Iï¿½Lï¿½ï¿½ï¿½ï¿½ï¿½%0<LÇ¥[email protected] -ï¿½ï¿½ ï¿½ï¿½%0: r ï¿½Nï¿½"c3ï¿½ï¿½ï¿½ï¿½ï¿½5ï¿½@.ï¿½ï¿½IgÒµï¿½ï¿½z[ï¿½Qï¿½ï¿½~ï¿½{ï¿½ï¿½ï¿½fï¿½9ï¿½%x(r)-ï¿½Hï¿½zï¿½nï¿½,"` *-"OFï¿½Qï¿½Lï¿½Eï¿½ï¿½ï¿½ï¿½d2I~%ï¿½ï¿½-f96B.ï¿½ï¿½ï¿½0ï¿½ï¿½<;<ï¿½ï¿½ï¿½mKï¿½Dcï¿½ï¿½]Íµï¿½ï¿½'P"ï¿½ï¿½'r9ï¿½ï¿½X)ï¿½ï¿½fï¿½ï¿½ï¿½ï¿½1/4 Iï¿½Lï¿½hï¿½&P=f"ï¿½ï¿½ï¿½Czï¿½rï¿½Xï¿½jTï¿½",Rï¿½ï¿½ï¿½ï¿½ï¿½^ï¿½ ï¿½ O...{ï¿½ï¿½Rï¿½:~Ñ¡"(tm)jI^Onï¿½ï¿½Vï¿½6ï¿½ï¿½w3v{ï¿½{iï¿½yw\$-ï¿½ï¿½ï¿½TZ~ï¿½rï¿½+ï¿½-ï¿½sï¿½'ß£ï¿½ï¿½ï¿½ï¿½^ï¿½Hï¿½ï¿½Ì´<ï¿½Bï¿½ï¿½ï¿½È³ï¿½Ûe(r)Dï¿½4=Ö´ï¿½dï¿½ï¿½bï¿½ï¿½ï¿½N/(tm)!ï¿½^ï¿½*j"\$ï¿½Tï¿½mï¿½ï¿½ï¿½f+(c)}ï¿½ï¿½ï¿½ï¿½|ï¿½^W-ï¿½ï¿½ï¿½-Ø{ï¿½^tlvpUï¿½ï¿½1/4 1ï¿½\r\ï¿½ï¿½Eï¿½^1/2ï¿½ï¿½c"ï¿½XGUBHï¿½"h(tm)j ï¿½ï¿½ï¿½6ï¿½ï¿½'ï¿½ï¿½ï¿½ã¥µK3ï¿½Pï¿½ï¿½ï¿½kï¿½uuuï¿½K|u'`|ï¿½Ò´}ò-ï¿½3/4ï¿½-;=ï¿½ï¿½ï¿½V{ï¿½ï¿½(tm)8*8...ï¿½ï¿½ï¿½tï¿½ï¿½ï¿½"ï¿½n*ï¿½Ø¶1/2mh464ï¿½ï¿½ï¿½(ï¿½ï¿½ï¿½jï¿½f2(tm)D"!cï¿½ï¿½/g%ï¿½yW3×R#@ï¿½\$ï¿½ï¿½ï¿½wï¿½ï¿½<ï¿½(c)Êªï¿½6ï¿½ï¿½Cï¿½Dï¿½qï¿½ï¿½ï¿½ ^ï¿½=ï¿½[ï¿½U...sgï¿½jï¿½ï¿½ï¿½*Zï¿½I.Mï¿½6 ï¿½ï¿½ï¿½lï¿½ï¿½kn9Vï¿½ ]ï¿½?mï¿½ï¿½ï¿½ï¿½-Jï¿½ï¿½ï¿½ï¿½Aï¿½ï¿½ï¿½\"Fï¿½ï¿½ï¿½\}vvï¿½mO[z.ï¿½xï¿½lï¿½(c)( ï¿½ï¿½`1/4aKï¿½yï¿½ï¿½Sï¿½7g) ï¿½=ï¿½ï¿½JTH1/4N(ï¿½Wï¿½×¯_?(tm)ï¿½6ï¿½ï¿½ï¿½ï¿½ï¿½w\ï¿½ï¿½ï¿½Cï¿½hOï¿½6ï¿½ï¿½ï¿½Ý¢-hxï¿½aï¿½ï¿½"T(r)ï¿½kï¿½ï¿½c1/2cï¿½Æº~(c)vï¿½'ï¿½ï¿½gYc!"ï¿½_FmvWrtï¿½ï¿½ï¿½nï¿½ï¿½kï¿½ï¿½8Pxï¿½(r)ï¿½]NPUScï¿½ï¿½!Gï¿½B(ï¿½iï¿½2ï¿½;ï¿½ï¿½rTï¿½ &z-ï¿½ï¿½(rï¿½ï¿½(r)ï¿½eï¿½ï¿½'Õï¿½FA^Bï¿½nï¿½<ï¿½ï¿½TXsï¿½ï¿½ï¿½ï¿½MPAX,(r){Tï¿½ (ï¿½ï¿½O "ï¿½eï¿½ï¿½ï¿½ï¿½Hï¿½+]ï¿½ï¿½ï¿½ Jï¿½BÍ¹ï¿½Tï¿½ï¿½ï¿½lxï¿½ï¿½ï¿½]ï¿½ï¿½r%zEtï¿½{;|'c Qï¿½ï¿½ï¿½8ï¿½ï¿½"~ï¿½ï¿½......ï¿½ï¿½ï¿½ï¿½oï¿½3/4ï¿½3/4'wGï¿½ï¿½-ï¿½/ï¿½Vï¿½_ï¿½Nï¿½\$-ï¿½5ï¿½8ï¿½Rï¿½ï¿½>ï¿½.Τï¿½ï¿½Anï¿½ï¿½kï¿½...ï¿½BγQ ï¿½ï¿½Q<-ï¿½mï¿½ï¿½sï¿½3(tm)Aï¿½soï¿½ï¿½ï¿½... ï¿½nï¿½5LMï¿½SXï¿½ ï¿½}xnï¿½' ;"ï¿½3ï¿½9)Yï¿½ï¿½ï¿½ jkï¿½ï¿½ ï¿½Sï¿½ï¿½ j9ï¿½Yï¿½ï¿½ï¿½ï¿½ï¿½=ï¿½="!

2. Verify Newtons second law.

Time taken for wooden block to pass GATE 1 ( � 0.000002 s) ( T1 - t1 ) Time take for wooden block to pass GATE 2 ( � 0.000002 s)

1. Math Investigation - Properties of Quartics

- a2 = 0 We can find the roots of the function quadratic equation The ratio of PQ: QR: RS is therefore Divide by a to set QR equal to one: The ratio therefore is: If calculated, it simplifies to -0.62: 1: -0.62 and 1.62: 1: 1.62 6.

2. Investigating the Graphs of Sine Functions.

My conjecture of -1/2 sin x Justifying my conjecture of y= -2 sin x By comparing the true graph of y= -1/2 sin x and my conjecture of it, I can conclude that they are equal and therefore my conjecture for its transformations and its characteristics was right.

1. Investigating the Graphs of Sine Function.

transformation of the graph of y = sin x into the graph of y = 1/3 sin x which is a one way stretch transformation away from the x axis (i.e. invariant line: x axis) with stretch factor + 1/3.

2. Mathematics Higher Level Internal Assessment Investigating the Sin Curve

This tells us that all the values of would be half of what they were originally causing the curve to become narrower and therefore decreasing the period of the curve. On the other hand, when the value of is smaller than 1 a bigger value of would be required to get the same value of .

1. Music and Maths Investigation. Sine waves and harmony on the piano.

This frequency is a measure of pitch and is recorded in Hertz (Hz) or cycles per second. Each frequency can be graphed in a two-dimensional plane as a sinusoidal wave. We will observe a pattern in harmonic notes and chords through the ratio of periods of each graph.

2. SL Math IA: Fishing Rods

minimal sum of the deviations squared from a given set of data. In simple terms, it finds a function that will disregard any unnecessary noise in collected data results by finding a value that has the smallest amount of deviation from the majority of the data.

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the provided text is a student-written piece of work investigating the properties of the sine function and its transformations. it does not contain any specific mathematical questions or problems to solve. it is a descriptive and analytical exploration of how the sine function changes with different parameters, such as amplitude, period, and phase shift.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
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First, describe the content structure you found in 1-2 sentences.

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TYPE: <one of the following values>
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Math Investigation - Sine Law

Extracts from this document...

Introduction

Part 1

Look at the graphs of y = sin x

Compare the graphs of:

y = sin x

y = 2sin x

y = 1/3sin x

y = 5sin x

The difference between all these graphs is a variable known as A, or amplitude of wave.

When A > 1, the graph stretches vertically.

When 0 < A < 1, the graph compresses vertically.

Also, A is the number that manipulates how far the graph compresses or stretches to. For example, in the graph of y = 2sin x, the graph stretches out to +2 and down to -2. The characteristics of the waveform are altered because of this. The range of the graph is increased or decreased in conclusion.

The domain and range of the graphs are:

y = sin x

D: {x| xεR}

R: {y| -1 < y < 1, yεR}

y = 2sin x

D: {x| xεR}

R: {y| -2 < y < 2, yεR}

y = 1/3sin x

D: {x| xεR}

R: {y| -1/3 < y < 1/3, yεR}

y = 5sin x

Middle

y = sin x?

The C variable in y = sin (x + C) is a variable that creates a horizontal translation.

In example, if C is substituted with 90, the equation becomes y = sin (x + 90):

y = sin x

y = sin (x+90)

It is evident that the entire graph shifted to the left by 90 unit. This can conclude that the amount that the graph moves by is by C, except it moves the direction opposite to the symbol in front of it. In this case, C, 90, caused the graph to move to the left by 90. This said, if C was -90, the graph would move to the right by 90 units. The range for y = sin (x + C) is not affected by the translation.

The domain and range of the graphs are:

y = sin x

D: {x| xεR}

R: {y| -1 < y < 1, yεR}

y = sin (x+90)

D: {x| xεR}

R: {y| -2 < y < 2, yεR}

Part 3

Conclusion

+ 90o)

I predicted this function as a vertical stretch since A > 1. The C in the graph translates the line 90 units to the left. There is no D in this function.

D: {x| xεR}

R: {y| -3 < y < 3, yεR}

y = ½sin x + 3

I predicted this function as a vertical compression because A < 1. There is no C present in this function. The D in the function moves the line up 3 units on the y-axis.

D: {x| xεR}

R: {y| -2½ < y < 3½, yεR}

Part 5

The graph of y = cos xand the graph of y = sin xis almost the exact same thing. The only difference is that the same graph would be translated 90o to the left if it involved the cos function.

Essentially, cos (x) = sin (x +90o).

Since this is true, it is conclusive that sine is a very versatile function with many altering variables.

y = cos x

y = sin (x + 90o)

*Although it is not completely evident, the two lines are overlapping, as I had predicted.

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
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Related International Baccalaureate Maths essays

1. Extended Essay- Math

ï¿½_ï¿½ tIME ï¿½ 2-ï¿½ï¿½ IDATxï¿½ï¿½lgï¿½Ç.Hï¿½ï¿½Jï¿½ \$ï¿½Urï¿½vËªï¿½ZicÊªï¿½ï¿½ï¿½uï¿½ï¿½ï¿½Õï¿½ï¿½:ï¿½Iï¿½p"'ï¿½uï¿½n7ï¿½Sï¿½d"m"ï¿½ï¿½%]ï¿½\$T'J...ï¿½ï¿½ï¿½Ó¶8ï¿½cï¿½"ï¿½Ø¨EvUP-"8ZVï¿½hsï¿½dï¿½(tm)_-{Æï¿½ï¿½ï¿½(ï¿½ï¿½ï¿½xï¿½_ï¿½yï¿½ï¿½}çï¿½ï¿½Eï¿½\Ü§ï¿½[email protected]@ï¿½KPï¿½ï¿½[email protected]@ï¿½KPï¿½QSï¿½ï¿½Ô g:"ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½^ï¿½ï¿½ï¿½"4?cï¿½ï¿½dKï¿½^1/2ï¿½" ï¿½@ï¿½KPï¿½ï¿½[email protected]@ï¿½KPï¿½ï¿½[email protected]@Uï¿½T(ï¿½#ï¿½[ï¿½Õ¶Ö¦ï¿½!ï¿½ï¿½ï¿½ï¿½l - ï¿½ï¿½bï¿½Cï¿½ï¿½-ï¿½ï¿½6T5ï¿½Aï¿½ï¿½-ï¿½ï¿½Xï¿½ï¿½ Ú\ï¿½2 v5ï¿½ï¿½ï¿½ï¿½ï¿½ Pï¿½@.Aï¿½&ï¿½ï¿½ ï¿½"(c)ï¿½"ï¿½jï¿½ï¿½ Pï¿½@.ï¿½ï¿½Iï¿½Lï¿½ï¿½ï¿½ï¿½ï¿½%0<LÇ¥[email protected] -ï¿½ï¿½ ï¿½ï¿½%0: r ï¿½Nï¿½"c3ï¿½ï¿½ï¿½ï¿½ï¿½5ï¿½@.ï¿½ï¿½IgÒµï¿½ï¿½z[ï¿½Qï¿½ï¿½~ï¿½{ï¿½ï¿½ï¿½fï¿½9ï¿½%x(r)-ï¿½Hï¿½zï¿½nï¿½,"` *-"OFï¿½Qï¿½Lï¿½Eï¿½ï¿½ï¿½ï¿½d2I~%ï¿½ï¿½-f96B.ï¿½ï¿½ï¿½0ï¿½ï¿½<;<ï¿½ï¿½ï¿½mKï¿½Dcï¿½ï¿½]Íµï¿½ï¿½'P"ï¿½ï¿½'r9ï¿½ï¿½X)ï¿½ï¿½fï¿½ï¿½ï¿½ï¿½1/4 Iï¿½Lï¿½hï¿½&P=f"ï¿½ï¿½ï¿½Czï¿½rï¿½Xï¿½jTï¿½",Rï¿½ï¿½ï¿½ï¿½ï¿½^ï¿½ ï¿½ O...{ï¿½ï¿½Rï¿½:~Ñ¡"(tm)jI^Onï¿½ï¿½Vï¿½6ï¿½ï¿½w3v{ï¿½{iï¿½yw\$-ï¿½ï¿½ï¿½TZ~ï¿½rï¿½+ï¿½-ï¿½sï¿½'ß£ï¿½ï¿½ï¿½ï¿½^ï¿½Hï¿½ï¿½Ì´<ï¿½Bï¿½ï¿½ï¿½È³ï¿½Ûe(r)Dï¿½4=Ö´ï¿½dï¿½ï¿½bï¿½ï¿½ï¿½N/(tm)!ï¿½^ï¿½*j"\$ï¿½Tï¿½mï¿½ï¿½ï¿½f+(c)}ï¿½ï¿½ï¿½ï¿½|ï¿½^W-ï¿½ï¿½ï¿½-Ø{ï¿½^tlvpUï¿½ï¿½1/4 1ï¿½\r\ï¿½ï¿½Eï¿½^1/2ï¿½ï¿½c"ï¿½XGUBHï¿½"h(tm)j ï¿½ï¿½ï¿½6ï¿½ï¿½'ï¿½ï¿½ï¿½ã¥µK3ï¿½Pï¿½ï¿½ï¿½kï¿½uuuï¿½K|u'`|ï¿½Ò´}ò-ï¿½3/4ï¿½-;=ï¿½ï¿½ï¿½V{ï¿½ï¿½(tm)8*8...ï¿½ï¿½ï¿½tï¿½ï¿½ï¿½"ï¿½n*ï¿½Ø¶1/2mh464ï¿½ï¿½ï¿½(ï¿½ï¿½ï¿½jï¿½f2(tm)D"!cï¿½ï¿½/g%ï¿½yW3×R#@ï¿½\$ï¿½ï¿½ï¿½wï¿½ï¿½<ï¿½(c)Êªï¿½6ï¿½ï¿½Cï¿½Dï¿½qï¿½ï¿½ï¿½ ^ï¿½=ï¿½[ï¿½U...sgï¿½jï¿½ï¿½ï¿½*Zï¿½I.Mï¿½6 ï¿½ï¿½ï¿½lï¿½ï¿½kn9Vï¿½ ]ï¿½?mï¿½ï¿½ï¿½ï¿½-Jï¿½ï¿½ï¿½ï¿½Aï¿½ï¿½ï¿½\"Fï¿½ï¿½ï¿½\}vvï¿½mO[z.ï¿½xï¿½lï¿½(c)( ï¿½ï¿½`1/4aKï¿½yï¿½ï¿½Sï¿½7g) ï¿½=ï¿½ï¿½JTH1/4N(ï¿½Wï¿½×¯_?(tm)ï¿½6ï¿½ï¿½ï¿½ï¿½ï¿½w\ï¿½ï¿½ï¿½Cï¿½hOï¿½6ï¿½ï¿½ï¿½Ý¢-hxï¿½aï¿½ï¿½"T(r)ï¿½kï¿½ï¿½c1/2cï¿½Æº~(c)vï¿½'ï¿½ï¿½gYc!"ï¿½_FmvWrtï¿½ï¿½ï¿½nï¿½ï¿½kï¿½ï¿½8Pxï¿½(r)ï¿½]NPUScï¿½ï¿½!Gï¿½B(ï¿½iï¿½2ï¿½;ï¿½ï¿½rTï¿½ &z-ï¿½ï¿½(rï¿½ï¿½(r)ï¿½eï¿½ï¿½'Õï¿½FA^Bï¿½nï¿½<ï¿½ï¿½TXsï¿½ï¿½ï¿½ï¿½MPAX,(r){Tï¿½ (ï¿½ï¿½O "ï¿½eï¿½ï¿½ï¿½ï¿½Hï¿½+]ï¿½ï¿½ï¿½ Jï¿½BÍ¹ï¿½Tï¿½ï¿½ï¿½lxï¿½ï¿½ï¿½]ï¿½ï¿½r%zEtï¿½{;|'c Qï¿½ï¿½ï¿½8ï¿½ï¿½"~ï¿½ï¿½......ï¿½ï¿½ï¿½ï¿½oï¿½3/4ï¿½3/4'wGï¿½ï¿½-ï¿½/ï¿½Vï¿½_ï¿½Nï¿½\$-ï¿½5ï¿½8ï¿½Rï¿½ï¿½>ï¿½.Τï¿½ï¿½Anï¿½ï¿½kï¿½...ï¿½BγQ ï¿½ï¿½Q<-ï¿½mï¿½ï¿½sï¿½3(tm)Aï¿½soï¿½ï¿½ï¿½... ï¿½nï¿½5LMï¿½SXï¿½ ï¿½}xnï¿½' ;"ï¿½3ï¿½9)Yï¿½ï¿½ï¿½ jkï¿½ï¿½ ï¿½Sï¿½ï¿½ j9ï¿½Yï¿½ï¿½ï¿½ï¿½ï¿½=ï¿½="!

2. Verify Newtons second law.

Time taken for wooden block to pass GATE 1 ( � 0.000002 s) ( T1 - t1 ) Time take for wooden block to pass GATE 2 ( � 0.000002 s)

1. Math Investigation - Properties of Quartics

- a2 = 0 We can find the roots of the function quadratic equation The ratio of PQ: QR: RS is therefore Divide by a to set QR equal to one: The ratio therefore is: If calculated, it simplifies to -0.62: 1: -0.62 and 1.62: 1: 1.62 6.

2. Investigating the Graphs of Sine Functions.

My conjecture of -1/2 sin x Justifying my conjecture of y= -2 sin x By comparing the true graph of y= -1/2 sin x and my conjecture of it, I can conclude that they are equal and therefore my conjecture for its transformations and its characteristics was right.

1. Investigating the Graphs of Sine Function.

transformation of the graph of y = sin x into the graph of y = 1/3 sin x which is a one way stretch transformation away from the x axis (i.e. invariant line: x axis) with stretch factor + 1/3.

2. Mathematics Higher Level Internal Assessment Investigating the Sin Curve

This tells us that all the values of would be half of what they were originally causing the curve to become narrower and therefore decreasing the period of the curve. On the other hand, when the value of is smaller than 1 a bigger value of would be required to get the same value of .

1. Music and Maths Investigation. Sine waves and harmony on the piano.

This frequency is a measure of pitch and is recorded in Hertz (Hz) or cycles per second. Each frequency can be graphed in a two-dimensional plane as a sinusoidal wave. We will observe a pattern in harmonic notes and chords through the ratio of periods of each graph.

2. SL Math IA: Fishing Rods

minimal sum of the deviations squared from a given set of data. In simple terms, it finds a function that will disregard any unnecessary noise in collected data results by finding a value that has the smallest amount of deviation from the majority of the data.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to
user
TYPE: NO_QUESTION

The provided text is a student-written piece of work investigating the properties of the sine function and its transformations. It does not contain any specific mathematical questions or problems to solve. It is a descriptive and analytical exploration of how the sine function changes with different parameters, such as amplitude, period, and phase shift.