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Investigating graph of trigonometric function

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Introduction

Investigating the graphs of trigonometric functions

Y=Sin x

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On the above, a normal sin curve on a scale of -2image15.pngimage15.png<x<2image15.pngimage15.png and -4<y<4

The curve shows an amplitude of 1 since the crest-the centreline gives a value of 1.

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Middle

image17.pngimage09.png

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Therefore, considering the formula Y=a sin bX + c, we find that the letter a modifies the amplitude of the curve. For instance, if we increase its value, the curve will vertically stretch with an amplitude of the same value. If however we reduce the value, then the curve will vertically contract with an amplitude of the same value. Finally, if we inverse the sign of the amplitude for example we change ‘a’ into ‘-a’, then the curve will reflect through the centreline.

If we consider an infinitely extended

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Conclusion

To conclude, we should say that we can predict the shape and position of the graph of y=Asin(B(x+C) from the above information on A, B and C. We could say anticipate the vertical stretch of the curve by modifying the magnitude of A and inverse it by making A negative. Also, we could increase or decrease the cycles of the curves according to its period by changing the value of B. Finally, we could decide the horizontal translation of the curve to the left by adding a given C value or to the right while subtracting a given value of C.

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