L> Assignment #1 Nikki MassonAssignment#1ByNikki MassonExploringthe Sin Curvey=asin(bx+c)To start off exploringthe sin curve, we will very first look at the graph of the functiony=sin(x).Information about functiony=sin(x):Range and also Domain:The variety of the role arethe values in the y-direction the the equation hits, i beg your pardon wouldbe the term <-1,1>. The domain is the set of all real numbers.Amplitude:In simple terms the amplitudeis the elevation of the curve. To calculate the amplitude that thecurve, that is half of the distance in between the maximum and minimumvalues. For y=sin(x), the maximum worth is 1 and also the minimum valueis -1, therefore the amplitude that the above curve is 1.The Period:The period of the sin curveis how countless radians that takes to finish one cycle, or the lenghof one cycle. Because that y=sin(x), the duration is native x=0 to x=2pi.Now we space readyto explore: y=a sin(bx+c)Part 1: experimenting differentvalues the aLet united state compare ours originalgraph the y=sin(x) to y=a sin(x) for different positive valuesof a, hold b and c continuous at b=c=0.By to compare the red and bluecurves come the purple, we observe that together a increases theheight is increasing and also as a decreases the elevation is decreasing.This means that a is an altering the amplitude that the curve.And by ours previous meaning of amplitude, this way that themaximum and also minimum values are additionally changing. As the worth ofa rises to 2 the maximum and minimum values also increaseto <-2,2>, and as a decreases come (1/2), the maximumand minimum worths decrease to <-(1/2),(1/2)>.Now let us look in ~ negativevalues that a and see just how -a affects the curve.As we deserve to see native the above graph, the negativevalue the a reflects the curve over the x-axis.Part 2: trying out differentvalues that bNext we will certainly examine how baffects our curve. Let us compare our initial graph the y=sin(x)toy=sin(bx) for different positivevalues the b, hold a and also c continuous ata=1 and also c=0.Well, the looks prefer b is affect theperiod that the curve. Remind the period is the variety of radiansit takes to finish one cycle, or the size it takes come completeone cycle. For y=sin(x) (purple curve) the duration is 2pi, butas b increases to 2 (red curve), climate the duration of y=sin(2x)becomes 4pi. For boosting values of b, the curve is stretched.A smaller number for b has the opposite impact on the curve,it shrinks the curve or renders the duration smaller. For y=sin((1/2)x),the period is pi.Part 3: exploring differentvalues of cLastly, we will compare ouroriginal graph of y=sin(x) come y=sin(x+c) for different positivevalues the c, hold a and b continuous ata=b=1.From our observations, thevalue that c is shifting the curve come the left by 1. So itlooks prefer the snucongo.orgfficient c shifts the curve come the leftor right.


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Now, let united state look at a an unfavorable value that c.When c is negative,the curve is shifted to the best by the amount of c. Inthe over graph the red curve is change to the appropriate by 1.Conclusions from exploringy=a sin(bx+c):The snucongo.orgfficient a changesthe elevation or amplitude of the curve and negative snucongo.orgfficientsof a reflect the curve over the x-axis.The snucongo.orgfficient b changesthe duration of the curve.The snucongo.orgfficient c shiftsthe curve to the best for an unfavorable values of c and also shiftsthe curve to the left for optimistic values of c.Return to key Page