You have the data of two measured variables x and y. According to a theory the v

Question

You have the data of two measured variables x and y. According to a theory the variables relate to each other as the non-linear functions shown below: a) y = Ax^3, b) y^3 = A squareroot x, c) y = A cos^2 x, where A is a constant. For each case, decide which variables you have to choose to plot so the expected graph is a straight line that passes through the origin. For instance if a theory predicted the following form, y = Ax^2, then by plotting y versus X^2 the resultant plot would be a straight line that passes through the origin.

Explanation / Answer

A) y2= Ax3 or y =A1/2 x3/2

Plotting y versus x3/2, the resultant plot would yield a straight line passing through the origin.

b) y3= Ax1/2 or y = A1/3 x1/6

Plotting y versus x1/6 the resultant plot would yield a straight line passing through the origin.

C) y= A cos2(x) or y= A (1-sin2(x)) or A-y=A sin2(x)

Plotting A-y versus sin2(x) the resultant plot would yield a straight line passing through the origin.

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