You have the data of two measured variables x and y Accordin

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.

Solution

A) y²= Ax³ or y =A^1/2 x^3/2

Plotting y versus x^3/2, the resultant plot would yield a straight line passing through the origin.

b) y³= Ax^1/2 or y = A^1/3 x^1/6

Plotting y versus x^1/6 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.