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

Math Investigation - Sine Law

Extracts from this document...


Part 1

Look at the graphs of y = sin x

Compare the graphs of:

y = sin x


y = 2sin x

y = 1/3sin ximage02.jpg


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

...read more.


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

...read more.


 + 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.

...read more.

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

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Extended Essay- Math

    �_� tIME � 2-�� IDATx��lg�Ç.H��J� $�Ur�v˪�Zicʪ���u���Õ��:�I�p"'�u�n7�S�d"m"��%]�$T'J...���Ӷ8�c�"�بEvUP-"8ZV�hs�d�(tm)_-{Æ���(���x�_�y��}ç��E�\ܧ�P-@.@�KP��E@.@�KP�QSï¿½ï¿½Ô g:"�� ����^���"4?c��dK�^1/2�" �@�KP��E@.@�KP��E@.@U�T(�#�[�ն֦�!����l - ��b�C��-��6T5�A��-��X�� Ú\�2 v5����� P�@.A�&�� �"(c)�"�j�� P�@.��I�L�����%0<LÇ¥-@ -�� ��%0: r �N�"c3�����5�@.��Igҵ��z[�Q��~�{���f�9�%x(r)-�H�z�n�,"` *-"OF�Q�L�E����d2I~%��-f96B.���0��<;<���mK�Dc��]͵��'P"��'r9��X)��f����1/4 I�L�h�&P=f"���Cz�r�X�jT�",R�����^� � O...{��R�:~Ñ¡"(tm)jI^On��V�6��w3v{�{i�yw$-���TZ~�r�+�-�s�'ߣ����^�H��̴<�B���ȳ�Ûe(r)D�4=ִ�d��b���N/(tm)!�^�*j"$�T�m���f+(c)}����|�^W-���-Ø{�^tlvpU��1/4 1�\r\��E�^1/2��c"�XGUBH�"h(tm)j ���6��'���㥵K3�P���k�uuu�K|u'`|�Ҵ}ò-�3/4�-;=���V{��(tm)8*8...���t���"�n*�ض1/2mh464���(���j�f2(tm)D"!c��/g%�yW3×R#@�$���w��<�(c)ʪ�6��C�D�q��� ^�=�[�U...sg�j���*Z�I.M�6 ���l��kn9V� ]�?m����-J����A���\"F���\}vv�mO[z.�x�l�(c)( ��`1/4aK�y��S�7g) �=��JTH1/4N(�W�ׯ_?(tm)�6�����w\���C�hO�6���ݢ-hx�a��"T(r)�k��c1/2c�ƺ~(c)v�'��gYc!"�_FmvWrt���n��k��8Px�(r)�]NPUSc��!G�B(�i�2�;��rT� &z-��(r��(r)�e��'Õ�FA^B�n�<��TXs����MPAX,(r){T� (��O "�e����H�+]��� J�B͹�T���lx���]��r%zEt�{;|'c Q���8��"~��......����o�3/4�3/4'wG��-�/�V�_�N�$-�5�8�R��>�.Τ��An��k�...�BγQ ��Q<-�m��s�3(tm)A�so���... �n�5LM�SX� �}xn�' ;"�3�9)Y��� jk�� �S�� j9�Y�����=�="!

  2. Mathematics Higher Level Internal Assessment Investigating the Sin Curve

    So far in this investigation we have been gathering the shape and look of the graph from just the equation, however we will now do it the other way around. We will find the equation of the curve from the graph.

  1. Artificial Intelligence &amp;amp; Math

    Solution outlined. The 'security feature' has not been explained. This solution would dramatically decrease the cost of computer infrastructure needed to sort through the raw data as much fewer ISP computers are needed. This effectively eliminates the problem of cost and still successfully monitors and raises warnings, as before, and it does not limit the user, ISP or Government.

  2. Function Transformation Investigation

    Note: When we say multiply, division is also implied because it just comes back to multiplying by the inverse. The same is when we talk about stretching a graph; compression of a graph is just the opposite. Once again, we can move on to another transformation in function graphs.

  1. 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)

  2. Math Investigation - Properties of Quartics

    will get 4 roots from the above equation; we already know two roots which are Q and R respectively. Therefore, to find out the other two roots we will use Synthetic Division. We can thus divide the function by the point Q with the X-value of 1 to acquire a

  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. SL Math IA: Fishing Rods

    would be a good representation of the original data points, but still has some error. We can further analyze these points by comparing the cubic and quadratic function to the original points by graphing them. See next page. By analyzing this graph, we can see that both the quadratic function

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work